Sauté onion in olive oil over medium heat 4 minutes until soft.
Add garlic and red pepper flakes. Stir 60 seconds without browning.
Add both tomatoes, herbs, sugar, salt, and pepper. Simmer uncovered 8 to 10 minutes.
Stir in heavy cream and Parmesan. Adjust seasoning and loosen with water if needed.
Add uncooked gnocchi, stir to coat, cover tightly and cook 5 to 6 minutes on medium-low.
Remove from heat. Tuck torn burrata into the sauce and rest 90 seconds to soften.
Finish with olive oil drizzle and fresh basil. Serve from the skillet.