Scrub grapefruit* with warm soapy water and pat dry. Using rasp or zester, remove rind from grapefruit to make about 15 mL (1 tbsp); set aside. Using serrated knife cut both ends off grapefruits. Using sawing motion cut white pith off and discard. Place grapefruit into small food processor or chopper and puree. Pour into fine mesh strainer and reserve pulp. Set juice aside for another use. (Or drink while making the biscotti.)
In a large bowl, using electric mixer, beat margarine and sugar together until fluffy. Beat in eggs, one at a time until combined. Beat in vanilla. Add grapefruit pulp and grated rind and beat until combined.
In another bowl, whisk together flour, bran, baking powder and soda and aniseed. Stir into margarine mixture with cranberries until soft sticky dough forms.
With floured hands, divide dough in half and roll each half on floured surface into twelve 30 cm (12 inch) log, about 5 cm (2 inches) wide and place both on large parchment paper lined baking sheet. Flatten logs slightly.
Bake in 180°C (350°F) oven for about 25 minutes or until golden and firm to the touch. Remove from oven; let cool for about 15 minutes. Transfer to cutting board and cut into 1 cm (½ inch) thick slices.
Stand biscotti slices upright on baking sheet, leaving some space between each and return to oven for about 20 minutes or until golden and crisp. Let cool completely.
*Grapefruit and grapefruit juice can interact with certain medications. Speak to your healthcare provider if you have concerns.