In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the broccoli florets, vegetable broth, smoked paprika, salt, and black pepper. Bring to a boil, then reduce heat and simmer for 15 minutes, or until the broccoli is tender.
Using an immersion blender, puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender.
Return the pureed soup to the pot over low heat. Stir in the shredded smoked Gouda cheese and heavy cream, mixing until the cheese is melted and the soup is creamy.
Add the lemon juice and stir to combine. Taste and adjust seasoning if necessary.
Serve hot, garnished with additional cheese or a sprinkle of smoked paprika if desired.