Add all of the pesto ingredients to a food processor. Blend until smooth or desired consistency is reached. Taste for seasoning, add additional salt and pepper if needed.
Bring a large pot of salted water to boil. Cook rigatoni according to package instructions to al dente, be careful to not overcook. Reserve some pasta water before draining.
Cut the burrata balls into wedges.
In a large skillet, add charred corn and halved tomatoes and warm through over medium-low heat. Add the drained pasta to corn and tomato mixture. Stir in desired amount of pesto (may not need all of it), coating all of the pasta. Add some of the reserved pasta water if needed to thin out. Stir in half of the burrata wedges. Once everything is warmed through, top with additional burrata wedges and allow to slightly melt into the dish. Garnish with the juice of fresh grilled lemon.
You can use various kinds of corn. I prefer the fire roasted corn from the freezer section, but it can be hard to find. If you cannot find that, I would also recommend grilling fresh ears of sweet corn, then cutting it off the cob, especially during sweet corn season! If neither of those are an option, use regular frozen corn and cook it in a skillet with a little olive oil until charred.