Coat a large sauté pan with olive oil and add the garlic and crushed red pepper. Bring the pan to a medium-high heat. When the garlic has turned a lovely golden brown color, remove it and discard. Add the tomatoes and half of the stock and season with salt. Simmer until the tomatoes have wilted and let off their juices, about 4 minutes. Add the corn and the remaining stock and simmer until the corn is cooked through, about 2 more minutes.
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 using tongs and add it to the sauté pan with the tomatoes and corn. Add about 1/2 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 parmigiano, basil and a big drizzle of olive oil. Stir or toss the pasta vigorously. Divide the pasta among bowls, sprinkle with a little more parmigiano and serve immediately.
Be sure to store tomatoes at room temperature -- refrigerating them can make them mealy. They'll continue ripening as they sit on the counter.