What is required of one who broke his oath on the Quran not to kiss a girl unless it is in a permissible way (halal), and then went back and kissed her?

It is not permissible to engage in an illicit relationship with a girl. You have broken your oath, and you must offer one expiation for breaking an oath, which is feeding ten poor people, or clothing them, or freeing a slave. If you are unable to do that, then fast for three days. Your feeling of pain may be a punishment for the sin, for no affliction descends except due to a sin, and none is removed except through repentance. The solution is to increase seeking forgiveness, sincere repentance, and fearing Allah.