Make the crust: Pulse flour and salt in a food processor. Add butter and pulse until the mixture is crumbly. Add water and vinegar and pulse until the mixture forms a ball. Remove from food processor and lay dough on a sheet of wax paper. Press to a flatten slightly. Top with another sheet of waxed paper and roll until about 1/4” thick. While you are rolling, occasionally remove top wax paper sheet and flip the dough over to remove the bottom waxed paper sheet so that it doesn’t stick. (Alternately, you can chill the dough for 1-2 hours until firm, then roll it out with a little flour. I don’t like the mess.)
Chill the rolled crust for at least 30 minutes while you make the cookie dough.
Make the cookie dough: cream the butter and sugar together using a stand or a hand mixer. Beat in egg, butter and vanilla extract, baking powder, and salt. Add the flour and mix until a dough forms. Stir in sprinkles.
Remove chilled crust from refrigerator. Use a large circle cookie cutter to cut circles of dough. Gently press each circle into the bottom of a muffin pan that has been lined with cupcake liners. Add two tablespoons of cookie dough to each pie crust, pressing to level.
Chill pies for 30 minutes. Preheat the oven to 350°. Bake for about 22 minutes, until tops are just turning golden brown. Let cool completely before frosting.