Bring water to a boil. Bring a large pot of water to a rapid boil. Season generously with Kosher salt (a good 2 Tbsp).
Add pasta. Place DeLallo Pappardelle Egg Nest Pasta in the water, then use tongs or a spatula to break up the nests a bit. Cook for 9 minutes, until al dente.
Reserve cooking liquid. Before draining, reserve about ½ cup cooking liquid. Drain the pasta, then set aside.
Sauté the onion and corn. Heat 2 Tbsp olive oil in a large skillet over medium-high heat. Add red onion, then sauté until translucent, about 2 minutes. Add corn kernels, then season with 1 tsp Kosher salt and ¼ tsp black pepper. Sauté 3 minutes more.
Purée into a sauce. Transfer the corn kernels and red onion to a blender (or food processor fitted with blade attachment), reserving ¼ cup of corn -- set this aside. Add ⅓ cup mascarpone cheese and ½ cup packed basil. Blend until very smooth, about 20-30 seconds. Taste and adjust seasoning as needed.
Blister the tomatoes. Meanwhile, heat remaining 2 Tbsp olive oil in a large skillet (can use the same one as before!) over high heat. Add cherry tomatoes, season with ½ tsp Kosher salt, then cook until blistered, about 6-8 minutes, stirring often.
Toss together. Combine cooked pasta, blistered tomatoes, basil cream sauce, reserved corn kernels, and ¼ cup Parmigiano Reggiano in the large skillet over medium heat. Toss to thoroughly combine, the add ¼ cup of reserved pasta cooking water to thin out. Add more as needed. Give one final toss, then divide between bowls.
To serve: drizzle each serving with a little extra virgin olive oil, then add extra Parmesan, thinly sliced basil (if desired), and freshly cracked black pepper to taste. Serve with a generous pinch of flaky sea salt.