Brush 1 sheet of phyllo dough with melted butter and sprinkle with 1 tsp. sugar. Fit into a greased 10″ Springform pan, allowing the corners of the dough to hang over the edges.
Repeat step 1 using 3 more sheets phyllo, laying each sheet at a 45° angle from the last. Spread the cooked apples over the dough in an even layer.
Cut 3 sheets of phyllo dough in quarters, and working with 1 piece at a time, pinch at the center and flip over, so that the corners are pulled together and facing up. Place each crimped piece on top of the tart.
Repeat with the remaining quartered sheets of phyllo dough until the top of the tart is covered. Drizzle with the remaining butter and bake.