1Melt butter in a large pot over medium-high heat. Cook and stir onion in the melted butter until tender, 5 to 7 minutes.
2Sprinkle flour over the onion; continue cooking 2 to 3 minutes, stirring often.
3Pour chicken broth and milk into the pot; reduce heat to medium, and bring the mixture to a simmer. Stir shredded Gouda cheese into the liquid; cook and stir until the cheese melts completely.
4Place broccoli into a microwave-safe dish; cook in the microwave until softened, 3 to 5 minutes.
5Stir broccoli into the soup.
6Season the soup with nutmeg, salt, and black pepper to serve.