Observing voluntary fasting after the month of Ramadan helps one get closer to Allah. Fasting is very pleasing to Allah and it is one of the means of gaining abundant rewards and having sins forgiven.
Dr. Sano Koutoub Moustapha states that it is a noble act to sustain fasting as a habit after the month of Ramadan. However, it is good to know that there are specific days in which fasting are recommended outside the month of Ramadan such as six days of Shawwal, 13th, 14th and 15th of every month of Hijri calendar and Mondays and Thursdays of every week.
Therefore, a Muslim may consider fasting any of those recommended days by the Sharia.
May Allah bless us all and accept all our endeavors.