Heat oven to 400°F. Line a baking sheet with parchment paper and set aside.
Melt butter in a medium saucepan over medium heat. Add shallots, balsamic vinegar, and brown sugar and cook until the shallots are tender, 3 to 4 minutes. Stir in plums, rosemary, and salt and reduce heat to low. Cook until the plums are tender, stirring often, 20 minutes. Remove from heat and set aside to cool slightly.
Whisk the egg and milk in a small bowl and set aside.
Unfold one sheet of puff pastry onto a generously floured work surface. Using a floured rolling pin, slightly flatten the puff pastry. Using a knife or pizza cutter, cut the sheet into 12 rectangles. Repeat with the second sheet, rolling it to the same size before cutting.
Arrange 12 of the rectangles onto the prepared pan. Evenly sprinkle provolone onto each rectangle, leaving a ½-inch margin. Top each with 2 tablespoons compote and evenly distribute. Lightly brush the edges with egg wash.
Layer the remaining puff pastry rectangles on top, lining up the edges and gently stretching if needed. Using the tines of a fork, crimp the borders. Cut two to three slits in the top of each pie and brush with egg wash.
Bake for 20 minutes, or until the tops are golden brown. Slightly cool before serving.
