Coat 18 wells in 2 standard (12-well) muffin pans with cooking spray.
Dust a work surface with all-purpose flour.
Place one pie dough on the work surface and roll out until just over ⅛-inch thick if needed.
Using a 3 ⅔- to 4-inch round cutter, cut as many rounds out of the dough as you can.
Repeat with the second pie dough.
Gather and re-roll the dough scraps as needed until you have 18 rounds.
(If at any point the dough is too soft to work with, refrigerate until firm before proceeding.)
Press a dough round into each well, pressing the center down first, then working your way up the sides to press the dough all the way to the top of the pan.
Refrigerate for 20 minutes.
Meanwhile, heat the oven to 350°F.
Stir 1 stick room-temperature unsalted butter and 1 ½ cups packed light brown sugar together in a medium bowl with a sturdy spatula or wooden spoon until a thick paste forms.
Mix in 3 room-temperature large eggs one at a time, mixing until each is incorporated before adding the next.
Stir in ⅓ cup light corn syrup, 1 ½ teaspoons vanilla extract, 1 teaspoon kosher salt, and 1 teaspoon distilled white vinegar until smooth.
Divide the mixture between the tart shells (about 2 heaping tablespoons each).
Bake until golden, puffed, and bubbling, 20 to 22 minutes.
Let cool for 15 minutes.
Run a thin knife around each one to loosen.
Use a small offset spatula to transfer each tart from the pan to a wire rack.
Let cool completely, at least 45 minutes more.
If you’d like the filling to have a firmer texture, refrigerate before serving.
