In a medium bowl, beat the eggs with 1 tablespoon water and ¼ teaspoon each salt and pepper.
Heat 2 teaspoons of the oil in a large nonstick skillet over medium-high heat. Add the tomatoes and beans; cook, tossing occasionally, until warmed through, 1 to 2 minutes. Transfer to a plate and wipe the skillet clean. Heat the remaining teaspoon of oil in the skillet. Add the eggs and cook, stirring, until set but still soft, 1 to 2 minutes.
Serve the eggs topped with the tomato mixture and pesto, accompanied by the toast.