1 tablespoon extra-virgin olive oil
1 large onion, chopped
1 large carrot, diced
2 stalks celery, diced
1 large potato, peeled and diced
2 cloves garlic, minced
1 tablespoon all-purpose flour
1/2 teaspoon dry mustard
1/8 teaspoon cayenne pepper
2 14-ounce cans vegetable broth, or chicken broth
8 ounces broccoli crowns cut into 1-inch pieces, stems and florets separated
1 cup shredded Cheddar cheese
1/2 cup sour cream
1/8 teaspoon salt
Heat oil in a Dutch oven or large saucepan over medium-high heat. Add onion, carrot and celery; cook, stirring often, until the onion and celery soften, 5 to 6 minutes. Add potato and garlic; cook, stirring, for 2 minutes. Stir in flour, dry mustard and cayenne; cook, stirring often, for 2 minutes.
Add broth and broccoli stems; bring to a boil. Cover and reduce heat to medium. Simmer, stirring occasionally, for 10 minutes. Stir in florets; simmer, covered, until the broccoli is tender, about 10 minutes more. Transfer 2 cups of the chowder to a bowl and mash; return to the pan.
Stir in Cheddar and sour cream; cook over medium heat, stirring, until the cheese is melted and the chowder is heated through, about 2 minutes. Season with salt.