Sauté the Aromatics: Melt the butter in a large pot over medium-high heat. Add the chopped onion and sauté for 3-4 minutes until soft.

Add Garlic: After the onion softens, add the minced garlic and stir for another minute until fragrant.

Create the Roux: Whisk in the all-purpose flour and stir for 1-2 minutes until it turns light golden.

Add Stock: Gradually pour in the chicken or vegetable stock while whisking to prevent lumps. Bring to a boil for 3-4 minutes.

Incorporate Vegetables: Add the broccoli florets and carrots, reduce heat, cover, and simmer for 15 minutes.

Stir in Cream and Cheese: Add the half & half and cheddar cheese, stirring until the cheese melts.

Adjust Seasoning: Taste and season with kosher salt and black pepper as needed before serving.