Preheat oven to 400 degrees, and line a large baking sheet with parchment paper.

In a small skillet over medium-low heat, place the diced apple, cinnamon, lemon juice, brown sugar, butter and salt. Cook, stirring occasionally, until the apple softens and caramelizes, about 7 minutes.

Remove the apple mixture from the skillet and let cool while you work with the dough.

Roll our the dough into a 12-inch square on a floured surface. Use plenty of flour as you go, to prevent sticking.

Divide the apple mixture into four equal piles in the four corners of the dough, making sure to leave a 3/4-inch border from the edges of the dough. Cut the dough into four equal squares, the fold over diagonally to make four triangles. Crimp the edges closed with the tines of a fork.

Careful move the pies to the baking sheet, and brush with the beaten egg yolk. Sprinkle with coarse sugar, if using,

Bake for 20 minutes, until the pies are puffy and very golden brown. Serve warm.