Preheat oven to 400 degrees. On a lightly floured surface, roll out puff pastry into an 18-inch square. Trim into a 13-inch circle and cut a small X in center to vent. Transfer to a parchment-lined baking sheet and freeze 20 minutes.
In a 12-inch cast-iron skillet, melt butter over medium-high. Remove from heat. Sprinkle with sugar and salt; place plums, cut side down, in a single, snug layer.
Return to heat, bring to a rapid simmer, and cook, undisturbed, 7 minutes. Remove from heat and top with pastry. Bake until crust is deep golden brown and juices are thickened, about 35 minutes. Let cool on a wire rack, 10 minutes, then invert onto a platter. Serve warm.