With the tip of a small, sharp knife, cut out the cores of the tomatoes. Cut each tomato in half crosswise and, with a fingertip, scoop out and discard the seeds. Cut the tomatoes into rough 1⁄2-inch dice.

Scatter the bacon pieces evenly in a nonstick skillet and cook over medium-low heat until golden brown, about 5 minutes. With a slotted spoon, remove the bacon from the pan and drain on paper towels. Pour off almost all of the fat from the skillet, leaving just a thin glistening.

Return the skillet to medium-low heat and add the butter and shallots. Sauté until the butter has melted and the shallots begin to sizzle, about 2 minutes. Add the eggs and cook, stirring occasionally with a wooden spoon and scrape the bottom of the skillet, until the eggs form very moist, creamy curds. Stir in the tomato and bacon pieces, season to taste with salt and pepper, and continue cooking to your liking, taking care that the eggs remain on the soft and creamy side. Serve garnished with the basil.