In a large pot, melt 2 tablespoons of butter over medium heat until bubbly. Add 1 diced onion, 2 chopped carrots, and 2 chopped celery stalks, sautéing for about 10 minutes until the vegetables are soft and fragrant.

Stir in 3 minced garlic cloves and continue to cook for 1 minute, allowing the garlic to release its aroma. Then, sprinkle in 1 teaspoon of smoked paprika and 2 tablespoons of flour, stirring everything together for another minute.

Gradually pour in 4 cups of vegetable broth while whisking continuously to prevent lumps. Bring the mixture to a gentle simmer and cook for about 5 minutes until it starts to thicken.

Add 4 cups of chopped fresh broccoli to the pot and let it simmer for 8 to 9 minutes until tender. Stir occasionally to maintain the color and texture.

Reduce heat and blend the soup using an immersion blender until you reach your desired consistency. Alternatively, transfer the soup in batches to a countertop blender.

Once blended, stir in 1 cup of milk, 1 cup of cottage cheese, and 1.5 cups of shredded cheddar cheese, keeping the heat low while stirring until the cheese melts and the soup becomes creamy, about 3 to 5 minutes.

Taste your soup and adjust seasoning with salt and black pepper. Serve hot, optionally garnished with extra cheddar cheese or chives.