Cut the corn kernels off the cobs and transfer to a medium bowl. Using the back of the knife, scrape the cobs to release the corn milk into the bowl.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Add the tomatoes and cook until softened, about 3 minutes. Stir in the corn and corn milk, 1 tablespoon water, 3/4 teaspoon salt and a few grinds of pepper and cook until the kernels are tender,3 to 5 minutes. Remove from the heat and add the chives, basil and the remaining 1 tablespoon butter; toss to combine.