Warm a large pot over medium heat. Add the butter and olive oil. When the butter melts, add the onion and carrots. Cook for 5–6 minutes, stirring often, until the onion turns translucent and the carrots start to soften.

Stir in the garlic and cook for 30 seconds, just until fragrant. Do not let it brown.

Add the chopped broccoli, broth, smoked paprika, nutmeg, and a pinch of salt and pepper. Bring to a gentle boil, then lower to a simmer. Cook for 10–12 minutes, until the broccoli is very tender.

While the soup simmers, blend the cottage cheese and milk in a blender until completely smooth. This creates a creamy, high-protein base without heavy cream.

Optional thickener: Whisk the cornstarch into the milk-cottage cheese mixture until dissolved. This will give the soup extra body later.

Use an immersion blender to partially blend the soup in the pot. Leave some small pieces for texture. If you don’t have an immersion blender, transfer half the soup to a blender, blend until smooth, and return it to the pot.

Lower the heat to medium-low. Stir in the milk-cottage cheese mixture and the Dijon mustard. Let it warm gently for 2–3 minutes. Do not boil after this point.

Turn the heat to low. Add the grated cheddar by the handful, stirring slowly until melted and smooth. Keep the heat gentle to prevent the cheese from separating.

Remove from heat. Whisk in the Greek yogurt until fully incorporated. Taste and adjust with more salt, pepper, and chili flakes or hot sauce if you like a kick.

Let the soup rest for 5 minutes to thicken slightly. Ladle into bowls and garnish with a little extra cheddar, cracked pepper, or a drizzle of olive oil.