In a large pot, heat a tablespoon of olive oil over medium heat. Add the diced onion and cook for about 5–7 minutes or until they become translucent and fragrant.

Once the onions are softened, mix in the chopped potatoes and broccoli florets. Stir everything together and let it cook for an additional 3–4 minutes.

Pour in the vegetable (or chicken) broth, making sure the vegetables are fully submerged. Bring to a gentle boil, then lower the heat and let it simmer for about 15–20 minutes or until the potatoes and broccoli are tender.

Using an immersion blender, carefully puree the soup until you reach a smooth consistency. If you don’t have an immersion blender, you can transfer it to a countertop blender in batches. Just be sure to allow it to cool slightly before blending.

Return the blended soup to the pot over low heat. Stir in the heavy cream and shredded cheddar cheese, mixing until the cheese melts and the soup is creamy.

Season with salt, pepper, garlic powder, and paprika, stirring to combine. Serve hot and garnish with freshly chopped parsley or chives if desired.