Make the cookies: Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Whisk the flour, baking powder, salt and baking soda in a medium bowl. Melt the butter in a large microwave-safe bowl in the microwave. Whisk in the granulated sugar and eggs until smooth; whisk in the grapefruit and lemon zest. Stir in the flour mixture with a rubber spatula until just combined, then stir in the orange peel.
Divide the dough in half. Shape each piece into an 8-inch log about 2 inches wide on the prepared pan. Bake until golden, about 25 minutes. Let cool 10 minutes on the pan.
Reduce the oven temperature to 325 degrees F. Slice the logs crosswise 1/2 inch thick. Arrange the slices cut-side down on the same pan. Bake, rotating the pan once, until the cookies are dry, 30 to 35 minutes. Let cool completely on the pan.
Make the glaze: Heat the butter and vanilla pod and seeds in a skillet over medium heat until the butter sizzles, 1 to 2 minutes. Let cool slightly, then strain into a bowl. Whisk in the confectioners' sugar and 3 tablespoons heavy cream, thinning with the remaining 1 tablespoon cream if needed. Transfer to a small resealable plastic bag, snip a corner and pipe on the biscotti. Sprinkle with nonpareils. Let set, about 45 minutes.