Melt the butter in a large pot over medium heat. Add the diced onion, chopped carrots, and diced celery. Cook for 10 minutes, stirring frequently so the vegetables soften without browning.

Add the minced garlic to the cooked vegetables and sauté for 1 minute. Sprinkle in the smoked paprika and all-purpose flour, stirring constantly for another minute to coat the vegetables and form the base for thickening the soup.

Pour in the vegetable broth and add the chopped broccoli. Raise the heat to bring the soup to a gentle simmer. Cook for 8-9 minutes, or until the broccoli is softened but still bright green.

Lower the heat and stir in the milk. Once the soup is warm (do not simmer to avoid curdling), add the blended cottage cheese and the shredded cheddar cheese. Stir until the cheese is completely melted and the mixture is smooth. I like to keep the temperature low here to make sure the soup stays creamy and doesn’t split.

Transfer one cup of the soup to a blender, blending carefully and allowing the steam to escape, then return it to the pot. Alternatively, use an immersion blender to blend part of the soup directly in the pot for a smooth texture. Season to taste with salt and black pepper. I always taste and adjust salt at the end, as the cheese adds some saltiness on its own.