– 1 Tablespoon olive oil – 4 Tablespoons butter – 1 small yellow onion, finely chopped – 3 small or 2 large carrots, chopped small – 1 clove garlic, minced – 1/4 cup flour – 1 cup half and half – 4 cups low sodium chicken broth – Pinch nutmeg – Fresh black pepper – 2 large broccoli heads, florets and stems chopped (About 4 cups total) – 8 ounces (about 2 cups) sharp cheddar cheese, shredded – 2 (about 1/2 cup) ounces colby jack cheese, shredded – Salt to taste