1. Melt the butter in a 10-inch ovenproof skillet over medium-low heat. Remove from heat, and sprinkle sugar evenly over bottom of skillet. Starting at outside edge, arrange the plum halves in overlapping concentric circles, with cut sides somewhat perpendicular to the bottom of the skillet.

2. Return skillet to medium-low heat; cook until juices are bubbling and sugar is beginning to caramelize, 15 to 20 minutes. Holding fruit in place with a wide spatula, tilt skillet and drain syrup into a bowl; set syrup aside. If necessary, slide dislodged plums back into place. Let cool slightly, about 10 minutes.

3. Preheat oven to 400 degrees. On a lightly floured work surface, roll out sheet of pate sucree to a 10-inch square. Using an inverted 10-inch cake pan as a guide, cut out a circle. Place dough over plums, and prick dough all over with a fork. Bake in oven until crust is golden brown and juices are bubbling, 30 to 35 minutes. If top begins to brown too much before fruit is cooked through, cover it with a piece of aluminum foil.

4. Remove skillet from oven. Let cool 1 hour. When ready, place a serving plate, top side down, on tart, and quickly invert tart onto plate. If desired, reduce reserved syrup in a small saucepan over medium heat until thickened, about 5 minutes. Serve tart with warm sauce.