Melt butter in a 4-quart pot over medium heat. Cook onion for 5 minutes, then garlic for 30 seconds.
Add chopped broccoli, broth, salt and pepper. Bring to a simmer, cover and cook for 8 to 10 minutes until the broccoli is very tender.
Stir in milk and heat gently for 2 minutes. Sprinkle in potato flakes while stirring, then simmer gently for 1 minute until lightly thickened.
Switch off the heat and wait for bubbling to stop. Add cheddar in 4 small additions, stirring each one smooth before adding the next.
Stir in Dijon and divide among 4 bowls, keeping small broccoli pieces visible throughout the soup.