Heat the butter + olive oil in a large dutch oven or pot over medium heat. Add the onion + mushrooms and cook until tender, about 10 minutes. Whisk in the flour and cook until golden, 3 to 4 minutes, then gradually whisk in the milk and broth until smooth. Add the broccoli, carrots, bay leaves, thyme, cayenne and nutmeg, then season with salt and pepper. Bring to a simmer, reduce the heat to medium and cook, uncovered, until the broccoli is tender, about 15-20 minutes.