Bring a large pot of salted water to a boil. Cook pasta until 1 minute short of cooking time, according to the package directions. Drain, reserving ½ cup of pasta water.
While pasta is cooking, heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the prosciutto and cook (flipping occasionally) until the prosciutto browns in places and becomes crisp, about 5 minutes. Transfer the prosciutto to a large plate lined with paper towels.
Using the same skillet, heat 1 tablespoon of oil over medium heat. Add shallot and season with ½ teaspoon salt, and ¼ teaspoon black pepper; sauté 2-3 minutes. Add ¼ cup pasta water and all but ¼ cup corn; simmer until corn is heated through and almost tender, 3 to 5 minutes. Transfer corn mixture to a blender or food processor, and purée until smooth, adding a little extra water if needed.
Still using the same skillet, add butter and brown over medium-high heat, about 3-4 minutes. Add reserved ¼ cup corn and cook 1 to 2 minutes. Reduce heat to medium-low. Add cooked pasta, corn purée and ¼ cup of the pasta water. Toss to coat and cook for 30 seconds to heat and combine the flavors. Stir in the Parmesan, fresh basil, red pepper flakes, and fresh lemon juice. Check for seasoning and add more lemon juice, and salt + black pepper, to taste (if needed). Top with burrata (if using), prosciutto, additional fresh basil, and a drizzle of olive oil. Enjoy!
