Preheat oven to 400°F. Grease a 9-inch pie pan with butter.
Add dry ingredients for crust to food processor. Process until well-combined.
Add butter cubes to processor. Process until butter is incorporated into dry ingredients. The mixture should look crumbly.
Add in ¼ cup water and process until combined. Don't process it too long or the crust will become tough. Transfer to a large bowl. Add in another ¼ cup water and combine by hand. Knead until a dough forms but don't overdo it. You may need more or less water depending on the butter you use.
Form the dough into 2 discs, one slightly larger than the other. Wrap in plastic wrap and chill for 1 hour before rolling.
Combine flour, sugar, nutmeg, cinnamon, and salt in a small bowl. Toss with apples until well-combined. Set aside.
Roll larger disc of dough into a circle on a lightly floured surface. Place in bottom of pie pan and press into the edges of the pan.
Add apple mixture to pie pan. Don't add the juice from the bottom of the bowl. The apples will create enough moisture for the filling during baking. Drizzle melted butter over apples.
Roll smaller disc of dough into a circle on a lightly floured surface. Place on top of apples. Cut off any excess pie dough around the edges and crimp the edges down. You can use your hands or a fork to seal the edges. Cut slits in the top for venting. Wrap strips of foil around the edges of the pan so the crust doesn't burn.
Bake for 50-55 minutes or until crust is golden brown and filling starts to bubble out of the vents. Remove foil.
While pie is baking, combine butter, brown sugar, and walnuts in a small saucepan. Heat until butter and sugar is melted. Add in half and half and continue cooking until bubbly.
Once the pie has finished baking, pour the caramel mixture over the pie. It helps to place the pie on a sheet pan to catch the excess caramel. Return to the oven and bake for 5 more minutes or until caramel is bubbly.
Let pie cool completely before slicing. Cut into 8 slices. Refrigerate leftovers. Enjoy!