Cut broccoli stalks from tops; peel fibrous outer layer from stalks and chop coarsely. Cut off flowers and put them aside.
In a pot, combine chopped stalks, garlic, onion, rice, hot pepper flakes and stock. Bring to a boil over high heat. Reduce heat, cover and boil gently for 10 minutes or until rice is almost tender. Add flowers and cook, covered, for about 5 minutes or just until broccoli is tender.
In a blender, purée a little at a time until smooth and return to pot, if necessary. Stir in milk. Heat over medium-low heat, stirring often, just until it’s steaming. Do not allow to boil. Stir in lemon juice and season to taste with salt and pepper.
Sprinkle each serving with the cubed Old Cheddar.