Add chopped onions, carrots and celery. Sauté on low heat until softened, about 5 minutes. Add garlic. Stir and cook for 1 minute longer.
Stir in flour, salt and pepper to the pot. Mix and stir.
Slowly add chicken broth, milk and potatoes. Turn heat to high until it comes to a boil. Cover and continue to cook on low until potatoes are softened, about 10-15 minutes.
Stir in broccoli florets. Sprinkle with salt and pepper to taste. Cook uncovered until broccoli is cooked, about 5 minutes. Add cheddar and stir until cheese is melted.
If you prefer a smooth consistency, blend with an immersion blender.