Preheat the broiler to high and make sure the rack is as close to the fire as possible.
Wipe down the mushroom caps with a damp tea towel to remove any excess debris. Place them onto a cookie sheet and liberally brush the outside of the cap with olive oil. Place the oiled side down.
In a small bowl, mix the mozzarella cheese, mashed chickpeas, and chopped garlic. Spoon 1/4 of the mixture into each mushroom cap.
Liberally sprinkle the tops with salt, pepper, and paprika.
Broil for 5 minutes or until the cheese has melted and the outside of the mushrooms begin to wilt. Remove from the oven and drizzle liberally with olive oil.
Squeeze a few lemon wedges over the caps and serve with the remaning wedges as garnish.