Wash and pit the peaches. You can peel them if you like, but I never bother. Mash half into a small bowl and slice the remaining half.
Whisk together the sugar, salt, smoked paprika, and tapioca flour in a medium bowl. Add the mashed peaches and stir in the mango juice. Let the mixture sit for 15 minutes, then fold in the sliced peaches.
Line a 9-inch pie plate with aluminum foil. Place the peach mixture into the foil and freeze until solid, 6 to 8 hours.
Once the filling is frozen, remove from the aluminum foil and wrap in plastic wrap and store in a freezer bag for up to 3 months.
To bake: Heat oven to 325°F.
Unroll first piece of dough and place into a 9-inch pie pan, making sure the dough reaches to the lip of the pie pan. Trim excess, if necessary. Prick the bottom and sides with a fork and set aside.
Unroll second piece of dough and cut into 1 1/8-inch-wide strips using a pizza cutter or sharp paring knife; you should end up with 9 to 10 strips.
Remove the frozen pie filling from the freezer and place into the prepared dough in the pan.
Build your lattice by laying 4 to 5 strips of dough in horizontal stripes across the top of the pie. Weave the remaining strips vertically into the horizontal strips, creating a basket-weave lattice. Crimp around the edge with a fork. If you refrigerated the lattice beforehand, place on top of the pie and leave at room temperature for 10 minutes before continuing.
Lightly brush the edge of the crust with the egg yolk and place pie on the bottom rack of the oven. Bake until the pie bubbles around the edges, about 1 hour 15 minutes
Place the pie on a rack and cool to room temperature before serving, 1 1/2 to 2 hours.