In a small mixing bowl, combine 2 tablespoons water, 1 tablespoon of the granulated sugar and the cinnamon with a fork until it resembles wet sand. Set aside.
In a stand mixer fitted with the paddle attachment, cream the butter and the remaining 2/3 cup granulated sugar until light in color. Beat in the vanilla and egg. Sift together the flour and salt. Slowly add the flour to the butter. Then add the chestnut meal and mix until a dough forms. With mixer on low speed, slowly add the cinnamon mixture 1 teaspoon at a time until all of the mixture is added. Mix until a swirl of the cinnamon sugar appears, about 10 seconds, and then turn the mixer off. Turn the dough out onto a sheet of plastic wrap and tightly wrap. Refrigerate the dough for at least 2 hours.
For the filling: Melt the brown sugar, butter, nutmeg and salt in a large high-sided saute pan. Add the apples and cook over medium heat. Add the sherry, then reduce the heat to low, and cook until the apples are tender, about 15 minutes. Stir in the pecans, then remove from the heat and set aside to cool completely. Fold the applesauce into the cooked apple mixture.
Preheat the oven to 350 degrees F and line a baking sheet with parchment paper.
Dust a flat surface with flour. Roll the dough until 1/8- to 1/4-inch thick. Using a 3-inch round dough cutter, cut out as many circles as you can, re-rolling any excess dough until it is all used up. Add a heaping teaspoon of the filling to the center of each dough circle. Fold the sides of a circle in three parts, pinching corners together as you go, to create a triangle with a window of filling in the center. Repeat for the remaining cookies. Place the cookies 1-inch apart on the prepared baking sheet and bake until golden brown, 15 to 20 minutes. Cool the cookies before serving.
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