Preheat oven to 325°F. Lightly grease a cookie sheet; set aside. In a large bowl stir together the all-purpose flour, whole wheat flour, brown sugar, baking powder, and salt until combined. Add the egg, milk, oil, and vanilla, stirring until a stiff dough forms.
Form dough into a log 12 inches long. Place on prepared sheet and flatten slightly until log is 2 inches wide. Bake until firm and lightly browned, 20 to 25 minutes. Cool on cookie sheet for 1 hour.
Using a serrated knife, cut log into 1/2-inch-thick slices. Arrange on the cookie sheet and return cookies to oven. Bake until slices are dry and crisp, 20 to 25 minutes, turning once. Remove to wire rack to cool completely. Makes 18 to 20 biscotti.
Store at room temperature for up to 3 days. To freeze, place in a resealable plastic freezer bag. Label and freeze for up to 3 months.