Place tomatoes in a baking dish with olive oil, sugar salt and pepper and bake at 425 for 20 minutes. Make the pesto in the food processor by combining the remaining ingredients (besides the burrata) while drizzling in olive oil until just smooth. After removing the tomatoes from the oven, add dollops of the pesto and mix. Once well mixed, add the burrata. It’ll melt in easily.
If you’re making this as a dip, you might want to drain some of the olive oil so it has a thicker consistency. Otherwise, serve over a shell pasta and grate extra parm on top!