Slice zucchini into ¼ thick rounds. Melt butter in sauté pan with olive oil over medium heat. When bubbling, add zucchini rounds and sauté, turning occasionally, until lightly browned, approximately 8-10 minutes. Add garlic, oregano, and salt and pepper to taste. Toss gently until garlic becomes fragrant, 1-2 minutes. Remove from heat and serve topped with grated Parmesan cheese.
For a more colorful side dish, substitute one yellow (also called summer) squash for one of the zucchini.