Arrange an oven rack in the center of the oven. Preheat the oven to 375 degrees F. Butter 6 (10-ounce) ramekins. Set aside.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender, stirring occasionally, about 8 minutes. Drain. Using 2 cooked lasagna noodles in an "x" shape, line each ramekin, pushing the noodles gently into the bottom of the ramekins, allowing any excess pasta to overhang on the sides.
In a food processor, blend the corn, cream and garlic until chunky. Add the mascarpone, 1 cup of the Pecorino Romano cheese, the lemon zest, salt, and pepper. Blend until smooth. Add the basil and pulse until just combined. Spoon 1/4 cup of the filling into the bottom of each ramekin and sprinkle with 2 tablespoons of the Provolone. Fold 2 overhanging pieces of pasta over the filling, (trim the ends of the pasta with scissors, if necessary). Add another 1/4 cup of filling to each ramekin and top with another 2 tablespoons Provolone. Fold over the 2 remaining overhanging pieces of pasta.
Spoon any remaining filling on top of the pasta. Sprinkle the tops with the remaining 1/2 cup Pecorino Romano and drizzle with olive oil. Arrange the ramekins on a baking sheet and bake until the tops are golden brown and the filling is bubbling, about 25 to 30 minutes. Cool for 10 minutes.
To serve: Run a knife around the edge of the ramekins to loosen the lasagnas. Unmold the lasagnas onto serving plates and serve.
Recipe courtesy of Giada De Laurentiis