Heat olive oil or butter in a large pot over medium heat
Add chopped onions and sauté for 3–4 minutes until soft
Stir in garlic and cook for 30 seconds until fragrant
Add chopped carrots and cook for another 2 minutes
Pour in broth and bring to a simmer
Add broccoli florets and cook for 8–10 minutes until tender
Reduce heat to low
Carefully blend half the soup using an immersion blender for creamy texture
Leave some chunks for texture
In a blender, combine cottage cheese (or Greek yogurt) with a bit of hot soup and blend smooth
Stir the blended mixture back into the pot
Add shredded cheddar cheese gradually, stirring until melted
Add milk if you prefer a thinner consistency
Season with salt, pepper, and paprika
Simmer for 2–3 minutes to combine flavors
Taste and adjust seasoning if needed
Serve hot