Line a large rimmed baking sheet with parchment paper.
Remove the pie crust from the fridge to soften slightly while you prepare the filling.
Peel and slice the persimmons into ¼-inch thick slices. Add into a bowl and add the sugar, lemon juice, vanilla, cornstarch and salt. Mix until evenly combined.
Roll out the prepared dough into a 13-inch circle on lightly floured counter, then transfer to prepared pan.
Using a slotted spoon, lift the persimmons from the bowl, letting the excess juice drain, and arrange them in the center of the dough, leaving a 2-inch border around the edge. Save the juices for later use.
Gently fold one edge of the dough up over the persimmons, about 2 inches at a time. Continue around the galette, overlapping the dough every couple of inches. Lightly pinch the pleats to secure, but avoid pressing the dough into the fruit.
Transfer the sheet pan to the fridge and chill while you preheat the oven. Adjust oven rack to lower-middle position and heat oven to 375 degrees.
Once preheated, mix 1 tablespoon of milk with 1 tablespoon of the saved persimmon juice in a small bowl. Brush the mixture over the folded edges of the crust, then sprinkle with sugar. Brush any remaining persimmon juices over the persimmons.
Bake until crust is deep golden brown and fruit is bubbling, 45 minutes to 55 minutes. Transfer the baking pan onto a wire rack to cool.
While the galette cools, combine the honey and 2 teaspoons of water in a small glass bowl. Microwave for 10 to 20 seconds or until bubbling. Brush over persimmons and the crust. Cool completey. Cut into wedges and serve with vanilla ice cream, if desired.