Rub both sides of the bread with garlic. Set aside the garlic. Heat the oil in a frying pan, fry the bread slices for approx. 2 mins. on each side, remove from the pan and set aside.
Heat the oil in a frying pan, press the garlic you set aside, add to the pan and sauté briefly. Add the asparagus and sauté for approx. 5 mins.
Spread the crostini with cream cheese, place asparagus and peppermint leaves on top, season.