Preheat the oven to 400°F (200°C).
On a lightly floured surface, roll out the pie crusts to 1/8-inch thickness. Using a 3 1/2-inch cookie cutter or cup, cut out 18 circles from the pie crusts. Re-roll any scraps of dough to cut out additional circles if needed.
Place each circle of pie crust into the 18 slots of 2 standard 12-count muffin pans. Gently press the dough down and around the sides to fit snugly in each cavity. Transfer the muffin pans to the refrigerator while you prepare the filling.
In a mixing bowl, whisk together the brown sugar, granulated sugar, pumpkin pie spice, and salt until well combined. Add the pumpkin puree, evaporated milk, egg, and vanilla extract, and whisk until fully combined.
Remove the muffin pans from the refrigerator. Evenly distribute the pumpkin pie filling between all 18 pie crusts in the muffin pans (about 2 tablespoons per pie crust).
Bake for 16-20 minutes, or until the tops of the mini pumpkin pies are set and the crust is lightly golden brown. Keep a close eye on them to avoid burning.
Remove from the oven and allow to cool on a wire rack for 30 minutes. Carefully remove the mini pies from the muffin pan and place them on the wire rack to cool completely.
Once cooled, place the mini pies in an airtight container and refrigerate for at least 3 hours or overnight.
Serve chilled or at room temperature, plain or topped with homemade whipped cream.