Prepare the vegetables: In a large pot, bring salted water to boil. Add broccoli, cauliflower, and potato (if using). Cook for 12-15 minutes until very tender. Drain well and set aside.
Sauté aromatics: In the same pot, heat butter over medium heat. Add diced shallot and cook for 3-4 minutes until softened. Add minced garlic and cook for another minute until fragrant.
Create the base: Add the cooked vegetables back to the pot along with the broth. Bring to a gentle simmer.
Blend for creaminess: Using an immersion blender, blend the soup until completely smooth. Alternatively, blend in batches using a high-powered blender (be careful with hot liquids).
Add the protein powerhouses: Stir in cottage cheese and blend again until completely smooth. The cottage cheese should disappear entirely into the soup.
Thicken the soup: In a small bowl, whisk tapioca flour with 3 tablespoons of milk until smooth. Stir this mixture into the soup along with the remaining milk.
Melt the cheese: Reduce heat to low. Gradually add grated cheddar cheese, stirring constantly until melted and smooth. Don't let the soup boil at this stage to prevent curdling.
Final touches: Remove from heat and stir in Greek yogurt. Season with salt, pepper, and a pinch of nutmeg if desired. Taste and adjust seasonings.
Serve immediately: Ladle into bowls and enjoy while hot with your favorite toppings.