In a small saucepan, melt the butter. Add sugar, lemon juice, nutmeg, cloves and cinnamon, whisk together, and cook for 1-2 minutes until all sugar is dissolved; set aside.
Prep the crust in a pie dish and preheat oven to 400F. Core the apples, then slice into thin rounds using a mandolin or knife. Cut the slices in half. Starting from the outside, place the apples skin side up, one slightly overlapping the next, working your way towards the center in a clockwise direction. Finish the center with the smallest pieces.
Pour the sugar & spice filling over the top of the pie. Brush the crush with the beaten egg. Bake for 25 minutes or until golden. Cool slightly to allow the filling to set, then serve.