Cut a 2-inch circle from the center of each bread slice; discard circles. Set slices aside. Brush 1 teaspoon oil in a medium skillet, and heat over medium heat until hot but not smoking. Lay bread slices in skillet. Reduce heat to medium-low.

Crack an egg into the hole of each bread slice, and sprinkle each with 1/8 teaspoon salt. Cook until bottom of eggs are set and golden brown, about 2 minutes. Flip; cook 2 minutes more for soft-cooked eggs, or 3 minutes more for slightly firmer.

Meanwhile, heat remaining 2 teaspoons oil in another medium skillet over medium heat. Add shallot; cook, stirring occasionally, until lightly browned, 2 to 3 minutes. Add tomatoes, and chile if desired; cook, tossing occasionally, until mixture is softened and fragrant, 3 minutes. Transfer to a small bowl; stir in cilantro. Discard chile. Divide salsa between egg sandwiches, and serve.