In a large pot, melt the butter over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Add the minced garlic and cook for an additional 1 minute.
1/4 cup butter, 1 small onion, 2 cloves garlic
Sprinkle the flour, cayenne pepper if using, nutmeg, black pepper, and salt, over the onion and garlic, and stir to combine. Cook for 1-2 minutes to cook off the raw flour taste.
1/4 cup all-purpose flour, 1/4 teaspoon nutmeg, 1/8 teaspoon cayenne pepper, 1/2 teaspoon salt, 1/4 teaspoon black pepper
Gradually whisk in the half-and-half and chicken or vegetable broth, stirring constantly to prevent lumps from forming.
3 cups half-and-half, 2 cups chicken or vegetable broth
Add the chopped broccoli florets, carrots, and celery to the pot. Bring the soup to a simmer and cook for 15-20 minutes, or until the broccoli is tender.
4 cups broccoli, 2 medium carrots, 2 medium celery sticks
Reduce the heat to low and add the cubed Velveeta cheese, stirring until melted and smooth.
8 oz Velveeta cheese, 6 oz shredded sharp cheddar cheese, 1/4 cup grated Parmesan cheese
Add the shredded cheddar cheese and grated Parmesan cheese, stirring until melted and well combined.
Taste the soup and adjust seasoning as needed. Serve and enjoy!