Combine butter, sugar, orange peel and vanilla in a large bowl. Mix until light and fluffy. Mix eggs in one at a time. Reduce speed to low, add nuts and mix. Sift together flour, baking soda, baking powder and salt into a bowl. Add flour mixture and mix just until combined. Cover and refrigerate for 1 hour.

Preheat oven to 350 degrees. Divide dough in quarters. Using lightly floured hands, roll each quarter on a lightly floured surface into a log 1 1/2 inches in diameter; these should be almost the length of the baking sheet. Arrange 2 logs on a parchment-covered baking sheet. Bake until lightly browned and firm to touch, about 30 minutes. Logs will spread during baking. Remove from oven and allow too cool for 5 minutes on the baking sheet.

Leave oven set at 350 degrees. Using a spatula carefully transfer logs to a work surface. Cut biscotti logs into 3/4-inch wide slices with a serrated knife, or an electric carving knife. Arrange slices, cut side down, on baking sheet, and bake for 15-20 minutes, turning once. Allow cookies to cool on baking racks.

To frost, melt some white chocolate chips or white almond bark in a double broiler, add 1 tablespoon fresh grated orange peel. Thin the chocolate slightly with water. Dip tops of cookies and arrange on parchment paper-covered baking sheet and allow them to cool for 3-4 hours to set.