A grinding apparatus for dispensing a dose of ground frozen material starting from a frozen block includes a grinding unit for grinding the frozen block in order to provide an amount of ground frozen material and a feeding unit for feeding the frozen block to the grinding unit. In particular, the feeding unit includes a feeding member that is adapted for moving frozen block for a desired predetermined grinding stroke against grinding unit such that a grinding length of block is ground. A grinding unit provides at least one grater and one motor for causing the grater to rotate. In order to obtain a desired weight of the dose, a volume of frozen material is calculated that corresponds to said weight, since the density of the frozen material is known.
