First, chop your onions and broccoli, and mince the garlic. I like to make sure the broccoli florets are bite-sized so they cook evenly. Fresh vegetables make the soup taste brighter than frozen ones.
Melt butter in a large pot over medium heat. Sauté onions and garlic until soft and fragrant. Then, sprinkle in the flour and stir for a couple of minutes to make a roux—it helps thicken the soup without lumps.
Slowly pour in the broth and half-and-half, whisking constantly. Add the broccoli florets, and let the soup simmer until the broccoli is tender. This usually takes about 10–12 minutes.
If you like a creamy texture, use an immersion blender to partially blend the soup. I like to leave some chunks for a more rustic feel. Be careful not to over-blend or it can become too thin.
Reduce the heat and gradually stir in the shredded cheddar cheese. Season with salt, pepper, and nutmeg. Make sure the heat is low to avoid curdling the cheese.
Once everything is melted and creamy, taste and adjust seasoning. Ladle the soup into bowls, and it’s ready to enjoy. I like topping mine with extra cheese or croutons for a little crunch.