Preheat the oven to 375 degrees F (190 degrees C).
Coat a large skillet with cooking spray and place over medium-high heat. Add onion, garlic, salt, and cayenne pepper. Cook and stir until slightly softened, 3 to 5 minutes. Reduce heat to medium-low. Cook, stirring frequently to ensure onion doesn't burn, until browned and caramelized, 20 to 25 minutes.
Transfer cooked onion to a bowl. Add cheese wedges, breaking them into pieces and stir until evenly melted and mixed.
Place tart shells on a baking sheet and fill evenly with onion mixture.
Bake in the preheated oven until shells are lightly browned, about 8 minutes.
