Melt butter in a medium saucepan. Sauté onion and red pepper in butter for 5-10 minutes until vegetables are starting to soften.
Sprinkle flour over the vegetable mixture and stir until flour is incorporated. Add the half & half, milk, and chicken stock and stir to combine.
Add the broccoli, carrots and celery. Cook over low heat 20-25 minutes.
Use an immersion blender until desired consistency. Return to heat and add the cheddar cheese. Stir until cheese is melted. Add salt and pepper to taste and serve warm.