Velvety cheddar broccoli soup combines sharp cheese with tender broccoli for a vegetarian-friendly, family comfort classic. This rich, satisfying bowl is a cozy lunch or dinner option.
In a large pot over medium heat, melt the butter until foaming but not browning.
Add diced onion and sliced carrot; sauté for 5-7 minutes until softened and translucent, stirring occasionally.
Sprinkle in the flour and cook, stirring constantly for 2-3 minutes to form a roux with no visible dry spots.
Slowly pour in the vegetable broth while whisking to prevent lumps, then add milk and ground mustard; increase heat to bring mixture just to a simmer.
Stir in broccoli florets and cook uncovered on medium-low for 12-15 minutes until broccoli is very tender but still bright green.
Turn heat to low, use an immersion blender to puree the soup to desired smoothness (or blend in batches in a blender).
Gradually add shredded cheddar cheese, stirring constantly until melted and soup is velvety. Do not allow soup to boil after adding cheese.
Season with kosher salt and black pepper; taste and adjust as needed. Serve hot, optionally with extra cheddar sprinkled on top.