Heat olive oil in a large pot over medium heat. Add onions, celery, and garlic. Cook and stir until vegetables being to soften, about 5 minutes. Add thyme, tarragon, and celery seed and cook for 30 more seconds.
Add the broth and potatoes. Bring to a boil and reduce heat to medium-low. Cover and simmer for 5 minutes. Add broccoli and simmer 5 - 7 more minutes, until broccoli and potatoes are tender.
Carefully transfer soup to a blender or food processor. Pulse until soup is coarsely pureed (it should still be a little bit chunky.) Return pureed soup to pot over low heat.
Whisk together milk and flour until smooth and add to soup. Increase heat to medium and cook until mixture is bubbly and has thickened, stirring constantly. Add both cheeses and sprinkle with fresh ground pepper. Heat until cheeses are melted.
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