In a large nonstick saucepan coated with cooking spray, saute onion and garlic until tender. Stir in flour until blended; cook for 1 minute. Gradually whisk in broth. Bring to a boil; cook and stir for 1-2 minutes or until slightly thickened.
Add the broccoli, tarragon, thyme and pepper; return to a boil. Reduce heat; cover and simmer for 10 minutes or until broccoli is tender. Add milk; cook, uncovered, 5 minutes longer. Remove from the heat; cool slightly.
In a blender, process soup until smooth. Return to pan and heat through (do not boil). Stir in 1/2 cup of cheese until melted. Sprinkle servings with remaining cheese.