Prep: Chop broccoli small. Heat a pot over medium.
Sauté (3 min): Melt butter. Add onion, carrot, and garlic. Cook until soft and fragrant.
Simmer (7–8 min): Pour in broth and add broccoli. Simmer until just tender.
Thicken (2–3 min): Flour: sprinkle in flour; whisk 1 minute, then simmer.
Finish (2–3 min): Lower heat. Stir in milk. Take pot off heat and add cheddar in handfuls until smooth. Season with salt, pepper, and nutmeg. Splash in lemon juice if you like.
Serve: Adjust thickness with a little broth if needed. Ladle and enjoy.