2 + 1/2 cups Extra Sharp Cheddar Cheese, plus more for garnish
Bread Bowls, for serving, optional
Melt the butter in a large, heavy-bottomed sauce pan. Add the olive oil and onion, cook until tender, about 5 minutes. Whisk in the flour and cook until golden, 3 to 4 minutes, then gradually whisk in the evaporated milk or half-and-half until smooth.
Add the chicken broth, broccoli, carrots bay leaf, and nutmeg, then season with salt and pepper and bring to a simmer. Reduce the heat to medium-low and cook, uncovered, until thickened, about 20 -25 minutes.
Discard the bay leaves. Puree the soup, carefully in batches in a blender until smooth or use an immersion blender and puree right in the pot; you'll still have flecks of carrot and broccoli. Return to the pot. Add the cheese to the soup and whisk over medium heat until melted.
Serve in bread bowls if desired with a garnish of cheese.