Melt the butter in a 3-quart saucepan over low heat. Add the flour, garlic powder, nutmeg, white pepper, and thyme. Mix well.
Gradually whisk in the broth and milk. Continue to cook until thickened, stirring constantly.
Add the broccoli and simmer for 10 minutes.
Remove the pan from the heat. Add the cream, Worcestershire sauce, hot pepper sauce, and the cheeses. Stir until the cheeses have melted.
