Cheesy Broccoli Cheddar Soup

Name: Cheesy Broccoli Cheddar Soup
Ingredients: 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