Mix flour, sugar and salt together. Blend cold butter cubes into dry ingredients using food processor, pastry blender or the butter knife method. Stop mixing when texture of flour changes from silky to mealy; a few larger chunks of butter may remain.
Make well in flour mixture. Drizzle vodka in while pulsing food processor or mixing with fork until incorporated. Check hydration of dough between each addition of water by gathering a small fistful; if it holds together, it’s ready. If the dough is still too dry, slowly add water 1 tablespoon at a time. Add only as much water as it takes to combine dough into a ball or disk.
Add grated cheddar, roughly blend until just incorporated. Form dough into two disks and wrap in plastic. Chill for at least 1 hour before next step.
Remove 1 dough disk from refrigerator and roll out onto a lightly floured surface into a 13" round about 1/4" - 1/8" thick. Gently transfer dough disk into pie plate, leaving 1" overhang all around. Tuck edge underneath itself. Place in fridge.
Peel and core apples, cut into 1/4" slices. Place in large mixing bowl and toss with lemon juice, sugar and cinnamon. Set aside for at least 15 minutes.
Preheat oven to 400° F. Pour apple filling into bottom shell, forming a mound that is taller in the center. Dot filling with 1- 2 tablespoons of small butter cubes.
Prepare egg wash by gently whisking egg. Brush thin layer of egg wash over top crust. Sprinkle with sparkling or turbinado sugar. Place pie plate on lined baking sheet for easier clean up.
Bake at 400° for 20 minutes, then lower temperature to 350° and bake another 30-45 minutes, rotating pan halfway through. Bake until filling is bubbly and crust turns a deep golden color. If needed, cover the edges or tent the pie to keep from over- browning. Cool 1 hour before cutting.