Melt the butter in a large pot over medium heat and sauté the diced onion, carrots, and celery for about 10 minutes, stirring occasionally to prevent sticking. Stir in the minced garlic and cook for another minute, allowing its aroma to release.

Sprinkle the smoked paprika and flour over the vegetables, stirring continuously to coat evenly. Gradually pour in the vegetable broth and add the chopped broccoli. Allow the mixture to come to a gentle simmer, cooking for 8–9 minutes until the broccoli becomes tender.

Reduce the heat to low and stir in the milk, ensuring the soup stays warm but does not boil. Add the blended cottage cheese and shredded cheddar, stirring gently until the cheeses are completely melted. Take care to avoid high heat, which could cause the milk to curdle.

For a creamier texture, blend one cup of the soup in a blender, allowing steam to escape through the vent, then return it to the pot. Alternatively, use an immersion blender to lightly purée the soup to your desired consistency.

Season with salt and pepper as needed before serving.