In a large skillet over medium heat, melt the butter with olive oil. Add the sliced onions and sprinkle with salt. Stir occasionally until onions are golden brown and caramelized, about 15-20 minutes.

While the onions are caramelizing, season the flank steak with salt and pepper. Cook the steak in a separate skillet or on a grill for about 4-6 minutes on each side. Once cooked, let the steak rest, then slice it thinly against the grain.

Add the beef broth and thyme to the skillet with the caramelized onions. Let it simmer for about 10 minutes until it thickens slightly.

Preheat your oven to broil. Arrange slices of French bread on a baking sheet. Top each slice with a spoonful of the onion mixture, a few slices of steak, and a generous sprinkle of Gruyère cheese.

Broil the arranged bruschetta in the oven for 2-4 minutes until the cheese is bubbly and golden. Watch closely to avoid burning.

Garnish with fresh parsley if desired and serve hot.