In a large pot or Dutch oven, heat the oil over medium heat. Add the diced onion and shredded carrot, and sauté for 5-7 minutes until softened. Add the minced garlic and cook for another minute until fragrant.

Pour in the broth and bring to a gentle simmer. Add the broccoli florets, smoked paprika, salt, and pepper. Stir, cover the pot, reduce heat to low, and simmer for 10-15 minutes until the broccoli is fork-tender.

While the soup simmers, combine the full-fat cottage cheese, nutritional yeast, and Dijon mustard in a blender. Blend on high until the mixture is completely smooth with no curds remaining.

Once the broccoli is tender, use an immersion blender to pulse the soup directly in the pot for a partially chunky texture. For a completely smooth soup, carefully transfer it in batches to the standing blender and blend until velvety, then return to the pot.

Turn the heat to the lowest possible setting. Stir the creamy cottage cheese mixture into the soup until fully incorporated. Then, add the shredded cheddar cheese one handful at a time, stirring gently after each addition until it has completely melted. Do not let the soup boil.

Taste the soup and adjust the seasoning with more salt and pepper if needed. Let it rest for a few minutes off the heat, then ladle into bowls and serve hot.