In a large pot, melt some butter or heat a splash of olive oil over medium heat. Add 1 diced onion and 2 minced garlic cloves, stirring gently for about 3–5 minutes until they become translucent and fragrant.

Add 4 cups of chopped fresh broccoli to the pot, stirring to combine with the aromatics. Cook for an additional 3–4 minutes.

Pour in 4 cups of vegetable or chicken broth, bring to a gentle simmer, cover, and cook for about 10–12 minutes.

Remove the pot from heat and blend the soup using an immersion blender until smooth.

Return the blended soup to low heat, stirring in 2 cups of shredded cheddar cheese until melted. Season with salt and pepper.

If desired, mix 2 tablespoons of cornstarch with an equal amount of water and stir into the pot, heating for another 2–3 minutes until thickened.

Ladle the soup into bowls and garnish with extra cheese, croutons, or chopped scallions.