Special equipment: a 3 3/4-inch round cookie cutter, a 2 1/2-inch round fluted cookie cutter and a 6-cup muffin tin
Position 2 oven racks to the top and bottom thirds of the oven and preheat to 400 degrees F. Line a baking sheet with parchment.
Roll the pie dough into a 13-inch round. Cut the pie dough into 6 rounds using a 3 3/4-inch round cookie cutter. Press each dough round into a muffin tin cup, making sure it covers the inside of the cup. Poke the rounds all over with a fork.
Bring the pie dough scraps together in a ball and re-roll into an 8-inch round. Cut into 6 rounds using a 2 1/2-inch round fluted cookie cutter. Using a paring knife, cut decorative slits into each fluted round and arrange on the prepared baking sheet. Brush with heavy cream and sprinkle with the coarse sugar. Bake the pie dough in the muffin tin and on the baking sheet until golden brown, about 10 minutes. Let cool completely.
Meanwhile, puree the cornstarch, 1/4 cup granulated sugar, half the strawberries and 1/4 cup water in a blender. Transfer to a small saucepan, bring to a boil over medium-high heat and cook, whisking constantly, until thick and glossy, about 30 seconds. Remove from the heat, let cool completely and fold in the remaining strawberries.
Whisk together the heavy cream and remaining 1 tablespoon granulated sugar in a medium bowl until soft peaks form.
Remove the pie crust cups from the muffin tin. Spoon the strawberry filling into the cups and top with the fluted rounds and whipped cream.