Combine all of the streusel ingredients in a small bowl and mix until well combined. Set aside.
For the Apple Filling
Toss the diced apples, lemon juice and sugar in a medium bowl until apples are well coated.
Grease a sheet pan with the 1/2 Tbsp butter and spread the apples evenly on top.
Bake at 400°F for 12 minutes. Let apples cool before filling tarts.
For the Dough
In a medium bowl, combine the flour and salt until well blended.
Using a pastry blender or two butter knives, cut in butter until mixture forms small pea-sized balls.
Slowly add water and toss mixture lightly with a fork until dough forms a single ball. If needed, add more water in very small increments until no dry ingredients left in bowl. (*see note below)
Chill dough for 20 minutes.
Divide dough into 3 equal portions.
Flour table well and roll out each portion of dough until approximately 1/4 inch thick. Use caution to ensure that dough does not stick to rolling pin or table. (Dust pin and table if dough begins to stick.) Each portion of dough should be approximately 8" in diameter.
Place 1/3 of the apple filling (~1 cup) in the center of each portion of dough, leaving approximately 1.5" border on all sides.
Sprinkle 1/3 (~1/4 cup) of the Streusel on top of the apples in each tart.
Gently fold edges of the dough partially over the apple filling. Crimp edges together to form the crust. Brush the outer edges of the crust with the beaten egg. Sprinkle generously with coarse sugar.
Bake on parchment-lined sheet pan at 400°F for 20-22 minutes, or until crust is golden brown in color.
Notes
Note regarding amount of water in the dough: Start with the smaller amount (1/8 cup) and gradually add more water as needed until the dough forms a single ball when compressed. The goal is to add only as much water as needed to hold the dough together. Sometimes this will be closer to 1/8 cup and other times it may be closer to 1/4 cup depending on humidity and other factors.