Instructions

1. Whisk together flour, sugar and salt. Add butter pieces and cut into the flour mixture using a pastry cutter or two knives until butter is in various sizes no larger than peas.
2. Fill a cup with iced water and using a measuring spoon, drizzle a tablespoon of water over the flour mixture. Toss with a fork to distribute the moisture. Repeat this process adding a tablespoon of water at a time and tossing the mixture until your mixture looks shaggy and there's no dry piles of flour at the bottom of the bowl; it shouldn't look wet. (See galette post for photos) You should be able to grab a handful of the mixture and squeeze it in your hands and have it hold together. For me, this can take anywhere between 5-8 Tablespoons of water. It varies each time I make it.
3. Bring the mixture together in a ball. Divide into 8 portions and cover with plastic wrap to keep it from drying out while you roll each portion.
4. Tear off two sheets of plastic wrap about 10" long. (You just need it to big enough to give yourself room to roll out the dough.) Take one portion of the dough, shape it into a ball and place it in the center of one of the sheets of plastic and cover it with the other, sandwiching the dough between the two sheets. Lightly press on the ball to flatten it into a disk.
5. Using a rolling pin, roll the dough into a 5" circle. Roll from the center out, easing up on the pressure as you near the edges so that you don't roll them too thin. Your rolling pin should not roll past the edge of the dough and back onto your counter. That would squeeze your dough into paper thinness. Think of the circle of dough like a clock and roll out to the 12 then pick it up and go back to center to roll down to the 6. Use the plastic wrap to pick up and rotate your dough to help you roll out to the different points on the circle. Always roll from the center out and resist the temptation to roll your pin back and forth. Lift the plastic wrap as necessary to release any places where it's stuck together and preventing the dough from rolling out. For this recipe, you don't have to worry that your dough is a perfect circle, but you do want it to be rolled out to a uniform thickness so that it bakes evenly.
6. When you've achieved your 5" circle, keep it sandwiched in the plastic wrap and place on a tray or flat surface in the refrigerator. Grab more plastic wrap and roll out the remaining portions of dough. Refrigerate for about an hour or two or overnight.
7. When you're ready to bake, preheat your oven to 375 degrees F. Line two large baking sheets with parchment.
8. Combine all of the filling ingredients, stirring to thoroughly combine. You can adjust the sugar to taste, remembering that you're going to have a caramel topping that will also add sweetness later.
9. Remove one piece of dough from the refrigerator, then peel off the plastic wrap and place the circle of dough onto your parchment lined baking sheet. (Place it wherever it's going to bake because it will be harder to move once you've filled it.)
10. Pile about 1/2 cup of your apple mixture in the center of the dough leaving about a 1" border of dough.
11. Fold the dough edges up and over the apples, pleating and pinching together as you go. Do not stretch the dough or press it into the filling. Just pleat it up and over the filling in whatever fashion you choose until you've completely encased the edges of your filling. Remember to press/lightly pinch the dough edges as you go to keep pleats together. Finish filling the rest of your crostatas removing just one piece of dough from the refrigerator at a time, so that the waiting pieces stay cold.
12. At this point, I like to pop the trays back into the refrigerator one more time, if my dough has gotten too soft/warm, just to make sure the butter is firm, about 30 minutes. You could also use the freezer to do this in less time. (If you think you're going to need this time to firm the butter up, wait to preheat your oven until after you put the filled pies into the refrigerator.)
13. Just before baking, brush the surface of the dough lightly with the beaten egg, then sprinkle the dough and top of the filling with a coarse, raw sugar.
14. Bake for about 30 minutes or until crust is completely golden and filling is bubbly.
15. While crostatas are baking, make caramel sauce. (Or, make it in advance and heat it up when serving.)
16. In a heavy bottomed sauce pan, heat the one cup of white sugar over medium heat. Do not touch the sugar until you see all of the sides begin to melt. They may already look like they're turning a deep caramel color. Don't let this process go too far or your sugar will burn. Once you see the melted sides, use a spoon or heat proof spatula to pull the melted sides into the center. Stir it frequently until it reaches a deep amber color and becomes syrupy, lowering the heat if necessary.
17. Once it becomes syrupy, remove the caramel from the heat and add the butter. Stir until it is completely melted. (See photos of this process here) You may have clumps of caramel that form. Don't worry about it. Add the cream and the salt and combine as best you can, then return to the heat, stirring frequently until the mixture completely combines. If you had any clumps of caramel, they should melt and combine with the butter and cream as you heat it. Once your sauce has come together, remove from heat. I had a few tiny clumps of caramel left, so I strained my mixture into a mason jar to remove them.
18. Drizzle warm caramel sauce over crostatas and serve.