A bran finishing process in grain milling employs a milling machine in which bran that contains some endosperm, including aleurone, is fed into an annular milling chamber defined on an inner side by an eccentric cylindrical rotor and on an outer side by a frame assembly that includes perforated screens and abrasive surfaces. Longitudinal lobes protrude radially from the rotor. The lobes compress the bran as they rotate, while the lesser diameter of the rotor between lobes allows the bran to decompress, causing bran particles to rub together for detaching endosperm from the bran by friction forces. Bran particles also rub against the abrasive surfaces for scraping endosperm off the bran. Air flows through the milling chamber and carries the endosperm through the perforated screens, while the bran particles are discharged without passing through the screens.