Bring a large pot of salted water to a boil.

Preheat a grill or grill pan to medium-high heat.

Brush the corn and zucchini with 2 tablespoons of olive oil. Grill the corn, turning occasionally, for 10–12 minutes or until lightly charred on all sides. Grill the zucchini for 2–3 minutes per side until tender and marked by the grill. Remove the vegetables from the grill and allow them to cool slightly. Cut the kernels from the corn cobs and chop the zucchini into bite-sized pieces.

Cook the pasta according to package directions until al dente. Before draining, reserve 1 cup of pasta water. Drain the pasta and set aside.

Heat the remaining 2 tablespoons olive oil in a large skillet over medium heat. Add the shallot and cook for 2–3 minutes until softened. Stir in the garlic and cook for 30 seconds. Add the lemon zest, lemon juice, salt, black pepper, and crushed red pepper flakes, if using. Stir in ½ cup reserved pasta water.

Add the cooked pasta, grilled corn, and grilled zucchini. Toss until everything is evenly coated. If needed, add more pasta water a few tablespoons at a time to create a light, silky sauce. Fold in the basil and parsley.

Transfer the pasta to a large serving platter. Place the burrata in the center of the pasta. Drizzle with balsamic glaze. Garnish with additional basil leaves, freshly cracked black pepper, and lemon wedges. Serve immediately, allowing guests to break into the burrata and mix the creamy center throughout the pasta.