Prep vegetables by chopping broccoli into small florets, dicing carrots, finely chopping onion, and mincing garlic. Set aside.

In a large pot over medium heat, add olive oil and sauté onion and garlic for 3-4 minutes until translucent.

Add diced carrots and broccoli florets, stirring occasionally for another 5 minutes until softened.

Pour in vegetable broth and chosen spices, bringing it to a simmer and cook uncovered for about 15 minutes until veggies are tender.

Remove pot from heat and use an immersion blender to pulse soup until desired creaminess is achieved, leaving some texture if preferred.

Return to low heat, stir in milk and cheese gradually, stirring continuously until melted smoothly into the soup.

Ladle soup into warm bowls, garnishing with extra cheddar and black pepper. Serve with crusty bread if desired.