Set an oven rack about 6 inches from the heat source and preheat the oven’s broiler. Grease an 8-inch baking pan.

Heat oil in a large skillet over medium-low heat. Add garlic; cook and stir until fragrant, about 1 minute. Add zucchini, oregano, salt, and black pepper. Increase heat to medium; cook and stir until zucchini is almost soft, about 7 minutes. Drain excess liquid.

Transfer zucchini mixture to the prepared baking pan; sprinkle Mexican cheese blend and Parmesan over zucchini.

Broil in the preheated oven until cheeses are melted and start to turn brown, about 7 minutes.