Melt butter with oil in an 8-quart stockpot on medium heat. Add onions and continually stir until tender and translucent. Do not brown the onions. Add beef broth and thyme. Season with salt and pepper, and simmer for 30 minutes.
Heat the oven broiler. Ladle soup into oven-safe serving bowls and place one Protein Bun on top of each. Layer each bun with a 1/2 slice of provolone, 1/2 slice Swiss and 1/2 tablespoon Parmesan cheese. Place bowls on the cookie sheet and broil in the preheated oven until cheese bubbles and browns slightly. Best served fresh.