Chop the onion and mince the garlic. Wash and cut the broccoli into florets and peel and dice the potatoes.

In a large pot, melt the butter over medium heat. Add the chopped onion and sauté until translucent, about 5. Stir in the minced garlic and cook for an additional minute.

Add the broccoli florets and diced potatoes to the pot. Pour in the vegetable broth and bring to a boil. Reduce heat and let simmer for 15-20 until the potatoes are tender.

Blend the soup until smooth using an immersion blender or countertop blender.

Return the blended soup to the pot. Stir in the heavy cream, shredded cheddar cheese, thyme, paprika, salt, and pepper. Cook over low heat until the cheese melts, about 5.

Taste the soup and adjust seasoning if necessary. Garnish with additional cheese or fresh herbs before serving.