A composite yet monolithic free abrasive grinding lap includes a sintered porous matrix of ceramic or metal material and a quantity of silicon filler material, substantially completely filling the pores of the sintered porous matrix preform at least throughout an effective region of the lap that is to come in contact with a workpiece to be acted upon by the lap. The lap may further have a multitude of abrasive particles embedded in the filler material at the effective region. The lap is made by first slip-casting a preform, then freezing and freeze-drying the same, followed by lightly sintering the dry preform into a porous matrix preform, bringing the temperature of the preform to above the melting point of the silicon filling material, and filling the pores with the filling material in its molten state.