Heat olive oil in a Dutch oven or large soup pot over medium heat.
Add the onion and garlic, and cook until the onion is translucent but not brown, about 3 minutes.
Stir in the flour and cook for one minute to form a paste. Gradually whisk in the milk and vegetable broth until the mixture is smooth and no lumps remain.
Add the bay leaves, nutmeg, salt, and pepper. Increase the heat to bring the soup to a boil.
Once boiling, cover the pot, reduce heat to a simmer, and cook for 20 minutes, stirring occasionally to prevent burning.
Remove and discard the bay leaves.
Add the chopped carrot and broccoli.
Cover and continue to simmer for about 15 minutes longer, or until the vegetables are fork-tender.
Remove the pot from the heat and stir in the nutritional yeast. Use an immersion blender to blend the soup directly in the pot until smooth and creamy. Alternatively, carefully transfer the soup in batches to a stand blender.
Ladle the hot soup into bowls and serve immediately.