Recommended fasts include Mondays/Thursdays, the three white days each month, six days of Shawwal, and আরাফাত/Ashura days — avoid fasting on Eid and Tashreeq days.
Voluntary fasting after হজ্জ is an excellent way to continue building on the spiritual foundation established during the হজ্জ. The most significant post-হজ্জ fasting opportunity is the six days of Shawwal — নবী করীম (সাল্লাল্লাহু আলাইহি ওয়া সাল্লাম) said: 'Whoever fasts Ramadan then follows it with six days of Shawwal, it is as if they fasted the entire year' (Muslim). Since হজ্জ occurs in Dhul Hijjah (after Shawwal), this applies if you fast the following Shawwal.
Year-round মুস্তাহাব fasts include: Mondays and Thursdays (নবী করীম's regular practice, as these are days when deeds are presented to Allah), the three white days of each lunar month (13th, 14th, and 15th — Ayyam al-Beed), the Day of আরাফাত (9th Dhul Hijjah, for non-হাজীগণ), and the Day of Ashura (10th Muharram, with the 9th or 11th). Important: fasting is prohibited on the two Eid days and the three days of Tashreeq (11th-13th Dhul Hijjah), so new হাজীগণ should not attempt to fast immediately after their হজ্জ rituals conclude.
Source: Sahih Muslim; Sunan al-Tirmidhi; Imam al-Nawawi, Riyad al-Salihin