Chop broccoli into small bite-size florets. Set aside.

Add olive oil to a large pot over medium-high heat. Add the chopped onion and sauté for 4-5 minutes, or until starting to soften. Stir occasionally. Add the chopped potato to the pot and continue to cook for an additional 4-5 minutes, stirring frequently. Add the minced garlic and cook for an additional 30 seconds. Sprinkle vegetables with flour and paprika and stir to combine. Add the water or vegetable broth to the pot with the chopped broccoli florets and bring to a boil. When boiling, reduce heat to low and simmer, covered, for approximately 20 minutes.

Meanwhile, prepare the broccolini. Preheat oven to 400 F and line a large baking sheet with parchment paper. Toss broccolini with olive oil and sprinkle with salt and pepper. Bake for approximately 15-20 minutes, or until broccoli is tender.

Puree the soup in batches using a high-speed blender, or use an immersion blender if you have one available. Return soup to the pot and add the shredded cheese. Stir well until cheese has melted and season with salt and pepper, to taste.

Serve each bowl topped with prepared broccolini and additional smoked gouda cheese, if desired.