Position a rack in the lower third of the oven and preheat to 400 degrees . In a large saucepan, cook the strawberries, sugar, cornstarch, lemon juice and vinegar over medium heat, stirring, until syrupy, about 7 minutes. Lower the heat and simmer, stirring, until reduced to about 1-1/4 cups, 10 to 15 minutes; let cool.
Meanwhile, on a lightly floured work surface, roll out the puff pastry into a 13-by-14-inch rectangle. Cut into a 12-inch round, using a 12-inch plate as a guide; transfer to a parchment-paper-lined baking sheet. Fold the edges of the pastry inward to form a half-inch rim and brush with the butter. Spread the strawberry mixture within the rim.
In a small bowl, combine the mascarpone and honey and dollop over the jam. Bake until the crust is golden, 22 to 25 minutes. Let cool, then sprinkle with the mint.