Heat oil and butter in a large skillet over medium heat until butter melted. Add zucchini, onion, bell pepper, and garlic; cook until zucchini begins to soften, about 5 minutes. Stir in corn, half-and-half, salt, and black pepper. Cover, reduce heat to low, and simmer 5 minutes.

Off heat, sprinkle Monterey Jack cheese over top. Cover skillet until cheese melts, 2 to 3 minutes.