In a bowl, mix eggs, milk, salt and pepper. In a skillet, heat oil at medium heat. Add the mixture of egg and cook, stirring often, until it makes big creamy pieces. Spread pesto in the panini, add scrambled eggs and garnish with slices of tomatoes and cheese.
Heat another large skillet or a skillet with ridges at medium heat. Add panini and cook, pushing them, for about 8 minutes or until golden and crispy and cheese has melted (flip them at mid cooking).