Bring a large pot of well-salted water to a boil.  Coat a large saute pan with olive oil and add the garlic and the crushed red pepper. Bring the pan to a medium-high heat. When the garlic has turned a golden brown, remove it and discard. Add the grape tomatoes, half the stock, and season with salt. Simmer the pan until the tomatoes have wilted and let off their juices. Add the corn and the remaining stock and simmer until the corn is cooked through.

While the corn is cooking add the pasta to the pot of salty boiling water. Cook the pasta until the water comes back to a rolling boil plus 1 minute. Remove the pasta from the water and add it to the pan with the tomatoes and corn. Add about a half a cup of the pasta cooking water and cook until the water has evaporated and the sauce clings to the pasta. Remove the pan from the heat. Toss in the cheese, basil and a big drizzle of olive oil. Stir or toss the pasta vigorously.