Get the veggies ready: Clean and chop the onion, carrot, and broccoli. Chop the garlic.
Sauté the veggies: In a big pot with a heavy bottom, melt the butter over medium heat. Cook the carrot and onion for four to five minutes, or until they start to soften.
Add the garlic: Add the minced garlic and sauté until fragrant, about 30 seconds.
Create the foundation: To eliminate the taste of raw flour, sprinkle the flour over the veggies and stir constantly for one to two minutes.
Pour in the broth: To avoid lumps, gradually add the vegetable or chicken broth while stirring.
Stir in the broccoli, paprika, onion powder, garlic powder, salt, and black pepper. Bring to a low simmer.
Cook: Simmer for ten to twelve minutes, or until the carrots and broccoli are soft but still have some firmness.
Add the cream and milk: After lowering the heat to low, mix in the heavy cream and milk. Gently warm for three to four minutes. Don't let it boil too quickly.
Put the cheese in there: Stir the shredded cheddar gradually until it melts completely and the soup is smooth, creamy, and cheesy.
Taste and adjust the seasoning before serving. If preferred, top with more cheddar and serve hot, sprinkled with fresh parsley.