There is no such thing as Shab-e-Barat in Islam, all narrations used to prove offering Nafil Salat on the night of 15th Shabaan & visiting graveyards are fabricated or unauthentic. If details are required, the same can be provided regarding such hadiths InshAllah, right now we are writing authentic narrations regarding Shabaan.

Aisha (RadiAllahu Tala Anha) says: “I have seen Prophet Muhammad (SallAllah-u-Alaihi-wa-Sallam) fast in the month of Ramadaan and I have seen him (SallAllah-u-Alaihi-wa-Sallam) fast a lot in Shabaan”
[Sahih Bukhari & Sahih Muslim]

Osama (RadiAllahu Tala Anho) says: I said Oh ! Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) I have never seen you keep so many fasts in any month in the months like in Shabaan.

Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam): This is the month in which people are unaware meaning between Rajab & Ramadaan, this is the month in which people ‘s deeds are ascended towards the Lord of the Worlds, so I want my deeds to be ascended at a time when I am fasting.
[Nasai, Behqi (Shuab-ul-Eman), Sanad: Sahih]

Abu Huraira (RadiAllahu Tala Anho) says: Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) said: when Shabaan reaches its half, don’t fast after it.
[Narrated in Tirmizi, Imam Tirmizi called this hadith Hassan Sahih]

We should fast a lot in Shabaan but not after the 15th.

Imran bin Hasban (RadiAllahu Tala Anho) says: Prophet (SallAllah-u-Alaihi-wa-Sallam) said to some person “Did you fast in the center of this month?”
He said: No

Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) said: When you are free of fasting of Ramadaan then fast for two days instead.”
[Sahih Muslim]

The 15th shabaan should be observed with a fast, if left then two should be kept in replacement after Ramadaan.

Aisha (RadiAllahu Tala Anho) says: Prophet of Allah (SallAllah-u-Alaihi-wa-Sallam) used to fast and we used to say he won’t do iftaar (meaning wouldn’t stop). Then he would do iftaar, when left fasting he would keep leaving and we then used to say he doesn’t have any intention of fasting. He (SallAllah-u-Alaihi-wa-Sallam) used to recite Surah Bani-Israel & Surah Az-Zumur every night (during the month of Shabaan).
[Musand Ahmad, Buloogh ul Amani 10/200, Sanad: Jaiyed]