For the Soup:

1. Heat the oil and the butter in a large pot over medium heat. Add the onion and cook for 5 minutes. Add the garlic and cook for another minute. Sprinkle the flour over everything and toss until everything is coated. Cook for a minute or so and then add the nutmeg.
2. Slowly stream in the broth, stirring constantly, and cook until the mixture thickens slightly.
3. Add the bay leaf, carrot, and broccoli and simmer until tender, about 10-15 minutes. Discard the bay leaf.
4. Stir in the milk, half-and-half, and cheeses. Stir constantly until the cheese is melted. If the mixture gets too thick, add a little bit more milk or broth. Season, to taste, with salt and pepper.

For the Croutons:

1. While the soup is simmering, preheat the oven to 350°F. Spread the cubed bread out on a baking sheet.
2. Melt the butter in a small saucepan, add the garlic, and cook until the butter is lightly golden brown and bubbly.
3. Pour the brown butter evenly over the croutons. Season with red pepper flakes, salt, and pepper.
4. Bake for 15-20 minutes, stirring once or twice, or until the croutons are crispy and golden brown.
5. Serve the soup topped with the croutons and extra cheese, if desired.