Spray a large skillet with cooking spray and heat over medium.
Crack eggs into a bowl and whisk together. Pour into hot skillet and cook until set, stirring frequently to scramble.
Peel mango and slice thinly. Preheat panini/sandwich press.
Top each of 4 bread slices with 1/4 of the eggs, a slice of cheese, some mango slices, 1 tablespoon of salsa, and another piece of bread.
Brush oil on the outsides of the bread (or spray with additional cooking spray) and place on a hot panini press. Cook until golden brown and cheese has melted.
Cool slightly, cutting each sandwich into quarters before serving.