**Ingredients:**
– 3 tablespoons butter
– 1 small yellow onion, diced
– 4 cloves garlic, minced
– 1/4 cup all-purpose flour
– 2 1/2 cups chicken or vegetable stock
– 2 cups half and half, at room temperature
– 2 cups broccoli florets, chopped
– 2 cups cauliflower florets, chopped
– 1 large carrot, shredded
– 1/2 teaspoon Dijon mustard
– 2 cups cheddar cheese, grated
– Kosher salt and freshly ground black pepper, to taste
**Instructions:**
1. **Melt the Butter:** In a large pot or Dutch oven, melt the butter over medium heat.
2. **Cook the Aromatics:** Add the diced onion and minced garlic to the pot. Cook, stirring occasionally, until the onions are soft and translucent, about 5-7 minutes.
3. **Make the Roux:** Sprinkle the flour over the onions and garlic, stirring constantly to combine. Cook for 1-2 minutes to create a roux, which will help thicken the soup.
4. **Add the Stock:** Gradually pour in the chicken or vegetable stock, whisking continuously to prevent lumps from forming. Bring the mixture to a simmer.
5. **Add Half and Half:** Stir in the half and half and bring the mixture back to a simmer, but do not let it boil.
6. **Cook the Vegetables:** Add the chopped broccoli, cauliflower, and shredded carrot to the pot. Cook for 10-12 minutes, or until the vegetables are tender.
7. **Add the Mustard and Cheese:** Stir in the Dijon mustard and grated cheddar cheese until the cheese is melted and the soup is smooth and creamy.
8. **Season and Serve:** Season with kosher salt and freshly ground black pepper to taste. Ladle the soup into bowls and serve hot, garnished with additional grated cheese if desired.
**Enjoy the comforting goodness of Broccoli Cauliflower Cheese Soup!**