Wash and dry 6 mason jars. Lightly butter the inside of each jar, focusing particularly on the bottom and sides.
In a large bowl, whisk together the flour, salt, and sugar. Add the cold cubed butter and use a pastry cutter or your fingertips to work it into the flour mixture until it resembles coarse crumbs with some pea-sized pieces remaining.
Gradually add ice water, one tablespoon at a time, mixing gently until the dough just comes together. Divide the dough into two portions, one slightly larger than the other (about 60/40 split). Flatten each into a disk, wrap in plastic, and refrigerate for at least 30 minutes.
Peel, core, and dice the apples into small, uniform ½-inch cubes. Toss the diced apples with sugar, lemon juice, cinnamon, nutmeg, cloves, and cornstarch in a large bowl until evenly coated.
In a large saucepan, melt the 2 tablespoons of butter over medium heat. Add the apple mixture and cook for about 5-7 minutes, stirring occasionally, until the apples begin to soften but still maintain their shape. Remove from heat and allow to cool slightly.
Preheat your oven to 375°F (190°C). Remove the larger dough disk from the refrigerator and roll it out on a floured surface to about ⅛-inch thickness. Cut out circles approximately 5 inches in diameter.
Carefully press each circle into a prepared mason jar, gently forming it to the bottom and sides while allowing some overhang.
Divide the apple filling evenly among the dough-lined jars. Leave about ½-inch of space at the top of each jar.
Roll out the remaining dough disk to the same thickness. Cut out circles slightly larger than the jar openings, or create decorative patterns like lattice strips or shapes.
Place your chosen top crust design on each jar, then seal by crimping the edges together with the bottom crust overhang. If using a full circle top, cut small vents to allow steam to escape during baking.
Whisk the egg with a tablespoon of water to create an egg wash. Brush the tops of each pie with the egg wash and sprinkle with turbinado sugar.
Place the jars on a baking sheet, spacing them at least 1 inch apart. Bake for 30-35 minutes, or until the crusts are golden brown and the filling is bubbling. If the edges begin to brown too quickly, cover them loosely with foil.
Allow the mini apple pies to cool on a wire rack for at least 30 minutes before serving.