Per History Beneath our Feet:
Brant, then called Midway Avenue, appears on a 1907 plat of B.L. Duke's Hammond Property along Fayetteville Road. There, it extended about 1,000 feet west from Fayetteville to a dead end and two blocks east to an Oriole Street (no longer in existence) through what is now the northern edge of N.C. Central University's campus.
Brant Street was taken over by North Carolina Central University in ~2005, when houses on both sides of the street were demolished for campus expansion; it it now a pedestrian walkway.