Heat the broth in a pot or saucepan large enough to fit the corn over medium-low heat to just below a simmer. Simmer the corn in the broth for 4 minutes and transfer to a plate; reserve the broth and keep it hot. Using a chef’s knife, slice the corn kernels off the cob into a large bowl (you should have about 1-1/4 cups).
In a heavy-based deep skillet or wide saucepan, melt the butter (or heat the oil) over medium heat. Add the shallot or onion and cook, stirring occasionally, until it’s translucent, about 2 minutes. Add the rice and stir until the grains are well coated with butter or oil. Pour in the wine, stir, and cook until the wine is absorbed, about 1 minute.
Ladle in about 1-1/2 cups of the hot broth, and cook, stirring occasionally, until absorbed, 3 to 5 minutes. Continue adding broth in 1/2-cup increments, stirring and simmering until it’s absorbed each time, at intervals of about 3 to 5 minutes.
While the rice is simmering, combine the tomatoes, extra-virgin olive oil, and 2 Tbs. of the basil in a small bowl. Season with salt and pepper and set aside.
When the rice is just barely tender, after about 16 minutes, stir in the corn. Continue adding more stock and stirring until the rice is creamy but still firm to the tooth, 20 to 25 minutes total. Remove from the heat, fold in the Parmigiano and then the tomato-basil mixture. Top each serving with the remaining basil and serve immediately.