Preheat oven to 425 degrees F. In a large skillet, heat oil over medium-high heat; add onions. Let onions cook at least 3 minutes before stirring (they should start to brown before you move them around). Continue to cook, stirring only occasionally, about 20 minutes, until onions are well browned. Add thyme and season with salt and pepper.
Spread bread slices with a little mustard. Divide onion mixture evenly over bread slices then top each with cheese.
Place on a foil-lined baking sheet; bake 10 minutes or until cheese is melted.