Heat olive oil in a medium pot over medium heat. Add chopped onion with a pinch of salt and cook until translucent, 6–8 minutes. Add minced garlic and cook 30 seconds until fragrant.
Add crushed tomatoes and broth. Bring to a gentle simmer, then reduce heat and cook 10–12 minutes to blend flavors. Stir in sugar if tomatoes are too acidic.
Remove from heat for a minute. Add cottage cheese and optional cream. Puree with an immersion blender or in batches in a countertop blender until smooth and velvety.
Return to low heat, stir in basil, and season with salt and pepper. Warm for 1–2 minutes and serve topped with fresh basil, a drizzle of olive oil, and crusty bread.
Notes
Use small-curd cottage cheese for the smoothest texture, but any type will work after blending.
Reheat gently—avoid boiling after adding dairy to prevent split textures.
Leftovers keep 3 days in the refrigerator; freeze for up to 2 months (thaw and blend before reheating).