Sprinkle 2 Tbs. cheese on half a tortilla. Top with 1 slice ham and 2 Tbs. cheese. Sprinkle with a pinch of smoked paprika then fold the other half of the tortilla over filling.
Heat 1 tsp. olive oil in a skillet over medium heat. Add one quesadilla, and cook until golden, about 2 minutes. turn and cook other side. Repeat steps to make one more quesadilla. Slice each quesadilla into 4 wedges.
Add 1/3 cup finely chopped cooked broccoli florets to the quesadilla before cooking.