Make the dough for the pappardelle. Sift the all-purpose flour and semolina flour on a large work surface. Create a well in the center and carefully crack the eggs into the well. Add the olive oil and using a fork, break up the eggs. Start dragging in the flour mixture into the well, gradually adding more flour. Mix until just combined.

Knead the dough until smooth and elastic, about 4-5 minutes. Cover the dough and let rest for 30 minutes. Roll out the dough either with a rolling pin or with a pasta machine. Cut the dough into ¾ inch thick noodles. Dust with semolina and cover with a clean kitchen towel until ready to cook.

Meanwhile, make the corn pesto. Place the corn, pine nuts, Parmesan, and olive oil in a food processor or blender until a paste forms. Season with salt and pepper. Set aside.

Preheat oven to 400 degrees F.

Lay prosciutto in an even layer on a lined baking sheet. Bake for 7-8 minutes or until crisp.

Heat 1 tablespoon oil in a medium saute pan over medium heat. Add the 2 ears shucked corn and saute for 3-4 minutes or until slightly charred. Remove from heat and keep warm.

In the same pan, heat another tablespoon of oil. Add the halved cherry tomatoes and cook until blistered and softened, about 5-7 minutes. Remove from heat and keep warm.

Boil a large pot of salted water on high heat. Cook the pappardelle for 2-3 minutes or until al dente. Drain, reserving ½ cup of the cooking liquid.

Add the pasta back to the pan along with the corn pesto, reserved cooking liquid, cooked corn, and ⅓ cup grated Parmesan. Stir to coat the noodles in the sauce and let simmer for about 2 minutes. Season with salt and pepper and portion the pasta into 4 bowls. Top with the cherry tomatoes, crispy prosciutto, fresh basil, and extra Parmesan. Serve.