In a medium-sized pot, melt one tablespoon of butter over medium heat and saute the diced onion until translucent. Add the garlic and cook for 30 seconds more until fragrant.

Add 2 more tablespoons of butter and let them melt over the sauteed veggies (be careful not to let the butter brown). Once the butter has melted, sprinkle the flour over it and cook this mixture for about 2 minutes, stirring constantly

Whisk in the vegetable stock and half and half until no lumps remain. Let this soup base simmer for about 15-20 minutes until it thickens

Throw in the broccoli florets and the sliced carrots and cook them for 15 more minutes until tender but still a little bit firm.

Stir in the chicken bouillon, paprika, salt, and pepper, and cook for about a minute more.

Remove from heat and add the freshly shredded cheddar. Stir until it’s all melted and serve the most amazing broccoli cheese soup while hot!