Melt butter in medium saucepan over medium high heat. Add in onions and cook, stirring frequently until soft, about 3 minutes. Add in garlic, dried thyme and flour, and cook for about 1 minute, stirring constantly. While whisking, slowly pour in milk, chicken broth and broccoli. Cook, stirring frequently, just until mixture begins to gently boil and thicken (if broccoli is not yet tender then reduce heat to medium-low and cook just until broccoli is tender. Stir in cream. Turn heat off, add in cheese and stir until melted, season with salt and pepper to taste. Serve warm.Recipe Source: Cooking Classy