Preheat oven to 350 degrees. Grease a rectangular baking sheet with butter. Cut 1/2 of an orange into chunks (include peel but not seeds) and puree until smooth.
In a mixing bowl, use an electric mixer to beat eggs and sugar until light and creamy. Add 1/2 cup of orange puree and vanilla and beat until fluffy (5 minutes).
Add butter, flour, baking powder, baking soda and salt. Only stir until combined. Stir in cranberries and walnuts.
On baking sheet, form dough into 3 long mounds. Wet hands and pat into flattened 12-inch logs (2-1/2 inches wide).
Bake logs at 350 degrees for 30 minutes or until golden. Cool for 10 minutes and transfer to cutting board.
Cut logs with a serrated knife into 1/2 inch thick slices. Arrange slices facing cut-sides down on two baking sheets. Bake at 350 degrees for 12 to 15 minutes or until golden. Cool on wire racks.
Store in air-tight container or freeze in plastic bags. Makes about 70 biscotti.