Melt butter in a 10-inch cast-iron or large, heavy skillet over medium heat. Stir in 3 tablespoons sugar; remove from heat. Arrange quince slices spokelike on top of butter mixture, working from center of pan to edge.
Combine 1 tablespoon sugar, honey, and juice, stirring well with a whisk. Drizzle mixture evenly over quince slices. Cover pan with foil; cook over medium heat 30 minutes.
Remove pan from heat; carefully remove foil. Cool 10 minutes.
Preheat oven to 400°.
Roll dough into an 11-inch circle; place over quince mixture. Tuck edges of crust into sides of pan. Cut 2 small slits in top of dough to allow steam to escape. Bake at 400° for 20 minutes or until lightly browned. Let stand 5 minutes. Place a plate upside down on top of pan, and invert onto plate. Serve warm.