Preheat your grill or smoker to medium heat (about 350°F/175°C).
In a large mixing bowl, combine the sliced peaches and lemon juice. Toss to coat the peaches evenly.
In a separate bowl, mix together the white granulated sugar, tapioca starch, vanilla extract, and smoked paprika (or regular paprika or cinnamon). Add this mixture to the peaches and gently stir until the peaches are well-coated.
Roll out one disc of pie crust and place it in a greased pie dish, ensuring it covers the bottom and sides evenly.
Pour the peach filling into the pie crust, spreading it out evenly.
Dot the diced unsalted butter over the peach filling, and sprinkle 1 tablespoon of white granulated sugar on top.
Roll out the second disc of pie crust and place it over the peach filling. Seal the edges by crimping with a fork or your fingers. Cut a few slits on the top crust to allow steam to escape.
In a small bowl, beat together the egg yolk and milk to create the egg wash. Brush the egg wash over the top crust for a golden finish.
Place the pie on the preheated grill or smoker and bake for about 40-45 minutes or until the crust is golden brown and the filling is bubbly.
Remove the pie from the grill/smoker and let it cool for at least 30 minutes before slicing.