Sauté the Aromatics: In a large pot, melt the butter over medium heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes. Add the minced garlic and cook for an additional minute.

Add Broccoli and Cauliflower: Add the broccoli and cauliflower florets to the pot and sauté for about 5 minutes, until they start to soften.

Add Broth: Pour in the chicken or vegetable broth, bringing the mixture to a boil. Reduce the heat to a simmer, cover the pot, and cook for 15-20 minutes, or until the vegetables are tender.

Blend the Soup: Using an immersion blender, blend the soup until smooth. If you prefer a chunkier texture, blend only half of the soup and leave the rest with some vegetable pieces.

Make the Cheese Base: In a separate saucepan, heat the milk over medium heat. In a small bowl, whisk together the flour and a few tablespoons of the warm milk to make a slurry. Slowly add the slurry back into the saucepan, whisking continuously until the mixture thickens.

Combine and Add Cheese: Pour the milk mixture into the blended soup, stirring to combine. Add the shredded cheddar cheese, heavy cream, salt, black pepper, and nutmeg (if using). Stir until the cheese is fully melted and the soup is well combined.

Adjust Seasoning and Serve: Taste the soup and adjust the seasoning if necessary. Serve hot, garnished with extra shredded cheddar cheese if desired.