Assalaamu alaykum. Is it obligatory or recommended to recite and reflect upon the Quran separately, as an act of worship outside of the prayer?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

Reciting the Quran and reflecting upon it outside of prayer is one of the best and most rewardable good deeds that draw the person closer to Allah; it is recommended for the Muslim to do this often, at all times and in all situations, to the best of his ability in order to earn the promised rewards. The Prophet, sallallahu ‘alayhi wa sallam, said, “Whoever recites a letter from the Book of Allah will be credited with a good deed, and a good deed merits a tenfold reward. I do not say that Alif-Laam-Meem is one letter, but Alif is a letter, Laam is a letter, and Meem is a letter.” [At-Tirmithi - Al-Albaani graded it saheeh (sound)] The Prophet, sallallahu ‘alayhi wa sallam, also said, “Read the Quran, for it will come as an intercessor for its reciters on the Day of Resurrection.” [Muslim]

Moreover, a stern warning is reported for forsaking the Quran and refraining from reciting it, reflecting upon it, and acting upon it. Allah, The Exalted, says (what means): {And the Messenger has said: “O my Lord, indeed my people have taken this Quran as (a thing) abandoned.”} [Quran 25:30]

Scholars held different views regarding the period in which the Muslim should complete reciting the whole Quran. Al-Haafith Ibn Hajar said:

“An-Nawawi underlined that the chosen opinion in this regard is that this (the period in which one should complete reciting the whole Quran) differs according to the person's circumstances and abilities. Some people require a longer time to understand and contemplate what they are reading. It is recommended for these people to recite the Quran at their own pace in a way that does not undermine their ability to reflect upon it and derive lessons from it. The same applies to the seekers of knowledge or those who have other responsibilities and duties pertaining to the religious affairs and public interests of Muslims; it is recommended for them to settle for reciting a portion (of the Quran) that does not undermine their performance of such tasks and duties. For any other Muslim, it is recommended to recite the Quran often to the best of their abilities without reaching boredom.” [Fat-h Al-Baari]

For more benefit, please, refer to fatwa 86568.

Allah knows best.