In a small saucepan, combine the milk, onion, garlic and nutmeg over medium-heat. Heat to 180°F. or until tiny bubbles form around edge (do not boil). Remove from heat; let stand 15 minutes.
Strain the milk mixture through a sieve into a bowl, reserving the milk. Discard the solids. Wipe the pan clean with paper towels; add the strained milk and flour to the pan, stirring with a whisk. Return the pan to medium heat; cook 2 minutes or until thick, stirring constantly with a whisk. Remove from heat. Add the cheeses, salt, and pepper, stirring with a whisk until smooth. Keep warm.
Cook the broccoli in boiling water for 3 minutes or until crisp-tender; drain. Top with cheese sauce; serve immediately.
Notes
If you wish to prepare this recipe as GLUTEN FREE, sub GF flour or an alternative thickener for the all-purpose flour.