Sauté the Aromatics:
Melt butter in a large pot or Dutch oven over medium heat. Add diced onion and sauté for 3–4 minutes, until softened.
Make the Roux:
Whisk in flour and cook for 1 minute to remove the raw flour taste.
Add Liquids:
Slowly pour in the broth while whisking to avoid lumps. Add the milk and stir until smooth.
Add Vegetables:
Stir in chopped broccoli and shredded carrots. Simmer uncovered for 15 minutes, or until broccoli is tender.
Add Cheese:
Remove from heat. Gradually stir in the shredded cheddar cheese until melted and smooth.
Blend (Optional):
For a creamier texture like Panera’s version, use an immersion blender to puree part or all of the soup.
Season and Serve:
Add salt, pepper, and nutmeg. Serve hot, topped with croutons or extra cheese.