Preheat oven to 425 degrees. On a floured work surface, roll out pie dough to a 1/8-inch thickness (or unfold store-bought dough). Invert a 9-inch plate on top of dough; trim dough around plate with a sharp paring knife to form a round (discard scraps, or save for another use). Refrigerate until needed.
Assemble the tart in a 10-inch cast-iron skillet. Press softened butter evenly into the bottom of the skillet, then sprinkle with the sugar. Arrange apple wedges in a circle around edge, then fill in the center with remaining wedges. Place skillet over medium heat, and cook until sugar mixture is light amber in color and bubbly, 8 to 10 minutes (syrup might brown unevenly).
Transfer to oven; cook until apples have softened, about 30 minutes. Carefully place dough round on top; bake until golden brown, about 15 minutes more.
Let cool, about 20 minutes. Run a knife around edge of skillet; invert tart onto a serving platter. Replace any apples that may have stuck to bottom of skillet; drizzle with any remaining pan juices. Serve warm or at room temperature.