In large skillet, heat oil over medium heat. Add onions and garlic; salt and pepper to taste. Cook, stirring occasionally, until onions are golden brown (about 15-20 minutes).
Add sherry or broth, half & half and thyme to onions; salt and pepper to taste. Simmer until sauce has thickened (about 2-3 minutes).
Serve caramelized onion sauce with grilled steak or chicken.