In a bowl, with an electric mixer on medium speed, beat butter and sugar until smooth. Beat in eggs, orange peel, and vanilla until well blended, scraping down sides of bowl as needed.
In another bowl, mix flour and baking powder. Stir or beat into butter mixture until well blended. Stir in hazelnuts.
Spoon 1 cup dough in dollops down the length of a buttered or cooking parchment-lined 12- by 15-inch baking sheet, 1 inch from edge. Spoon another 1 cup dough down the length of the other side of the sheet. With floured fingers, pat each strip of dough into a flat 13-inch loaf, about 1/2 inch thick and 2 inches wide. Repeat with remaining dough (dough can stand while first loaves bake).
Bake loaves in a 350° oven until golden, 15 to 20 minutes; if baking more than one pan at a time, switch pan positions halfway through baking.
With a sharp knife, cut loaves crosswise into 3/4-inch-thick slices. Separate slices slightly and tip each onto a cut side.
Return to oven and bake until cookies are slightly darker and firm and dry to the touch, 15 to 20 minutes longer. Gently slide biscotti onto racks to cool completely.
In a bowl set over a pan of barely simmering water (bottom of bowl should not touch water), stir chocolate chips often until melted and smooth, about 5 minutes. Spread chocolate on one side of each biscotti. Place cookies in a single layer, chocolate side up, on baking sheets, and chill until chocolate is firm, about 20 minutes.