Mix ancho chile powder, white sugar, brown sugar, salt, black pepper, cumin, dry mustard, cayenne pepper, and chipotle pepper in a small bowl until combined.
Place ribs meat-side down on aluminum foil. Prick back of rib rack several times with a knife.
Generously apply coating of dry rub to all sides of rib rack.
With rib rack meat-side down, fold foil around it to create a tight seal. Transfer to sheet pan.
Bake in preheated oven until tender and cooked through, about 2 hours. Remove and cool 15 minutes.
Increase oven temperature to 350 degrees F (175 degrees C).
Open foil, drain and discard any accumulated juices and fat. Brush barbeque sauce on all sides of rack.
Place rack meat-side up and return to oven, leaving foil open. Bake for 10 minutes, remove from oven, and brush another layer of barbeque sauce on meat-side only. Repeat baking and brushing with sauce 4 more times, for a total of 50 minutes baking time.
Cut rack into individual rib segments and serve with more barbeque sauce.