In a large nonstick saucepan coated with nonstick cooking spray, saute onion and garlic until tender. Add flour; stir to coat evenly and cook for 1 minute. Gradually whisk in broth. Bring to a boil; cook and stir for 102 minutes or until slightly thickened.
Add the broccoli, tarragon, thyme and pepper; return to a boil. Reduce heat; cover and simmer for about 10 minutes or until broccoli is tender. Add milk; cook, uncovered, 5 minutes longer. Remove from heat; cool to room temperature.
In small batches, transfer soup to a blender; cover and process until smooth. Return soup to pan; heat through. Reduce heat. Add 1 cup cheese; stir just until melted. Serve immediately. Garnish with remaining cheese.