Stir in the crushed tomatoes, vegetable broth, dried basil, sugar, and a sprinkle of salt and pepper. Bring to a gentle simmer and cook for 20 minutes.
Using an immersion blender, carefully blend the soup until smooth and creamy. Stir in the heavy cream and cheddar cheese until melted and well combined.
In a separate bowl, combine the flour, baking powder, garlic powder, and cayenne pepper. Cut in the cold butter until the mixture resembles coarse crumbs.
Stir in the milk until just combined, being careful not to overmix.
Spoon the dumpling batter into the simmering soup. Cover the pot and let cook for 15 minutes.
Serve hot, garnished with extra cheddar cheese if desired.
Notes
Leftovers can be stored in an airtight container in the fridge for up to 3 days. Add vegetable broth when reheating if needed.