Heat the oil and butter in a large skillet over medium heat.
Add the garlic, bell pepper, onion, and zucchini, and cook until the zucchini begins to soften, about 5 minutes. Stir in the salt, pepper, half and half, and corn. Cover, reduce heat to low, and simmer 5 minutes.
Remove from heat and sprinkle Monterey Jack cheese over top. Replace the cover on the skillet and allow to sit until the cheese melts, 2 to 3 minutes.