Creamy, cheesy, and dangerously easy to make.
Melt 4 tablespoons unsalted butter in a large heavy-bottomed saucepan over medium heat. Add 1 medium diced yellow onion, 1 teaspoon garlic powder, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper. Cook, stirring occasionally, until the onion is translucent, 2 to 3 minutes.
Sprinkle in 2 tablespoons all-purpose flour and cook, stirring often, until lightly browned, 1 to 2 minutes. Stir in 3 cups chopped broccoli florets, 2 cups half-and-half, 2 cups low-sodium chicken broth, 1 cup grated carrot, and 1/2 teaspoon Dijon mustard. Bring to a boil, stirring occasionally.
Reduce the heat to maintain a simmer and cook, stirring occasionally, until the broccoli is tender, about 5 minutes. Turn off the heat.
While stirring constantly, add 8 ounces shredded mild cheddar cheese a handful at a time, waiting until the cheese is completely melted before adding the next handful. Serve garnished with more shredded cheddar cheese and croutons if desired.