PREHEAT oven to 350° F. Line large baking sheet with parchment paper or grease well.
COMBINE flour, salt, baking powder and rosemary in medium bowl. Whisk 3 eggs and sugar in large bowl until well combined. Add olive and vegetable oils; whisk until well combined. With fork, add in flour mixture and 2/3 cup chunks; stir together to form a soft dough.
TURN dough out onto lightly floured surface. Knead dough lightly to bring together. (Dough will be slightly oily.) Divide dough in half. Roll each half into a log, about 16 inches long and 1 inch high.
PLACE each log onto prepared baking sheet. Press top of each lightly to flatten slightly. Beat remaining egg in small bowl. Brush top of each log with egg wash.
BAKE for 20 minutes or until lightly browned. Remove from tray from oven and place on wire rack for 15 to 20 minutes or until cool enough to handle.
PLACE logs on cutting board and diagonally slice each loaf into 3/4-inch slices. Place slices back on baking sheet, flat side down.
BAKE for an additional 4 minutes; turn each piece over. Bake for an additional 4 to 6 minutes or until dry. (Be careful to not overbake or the biscotti will become too hard.) Remove from baking sheet to wire rack(s) to cool completely.
LINE baking sheet with parchment or wax paper.
PLACE remaining chunks in small, uncovered microwave-safe bowl on HIGH (100%) power for 1 minute; STIR. Chunks may retain some of their original shape. If necessary, microwave at additional 10- to 15-second intervals; stirring until just melted. Dip one side of each biscotti in chocolate. Scrape along edge of bowl to remove excess chocolate. Place on prepared baking sheet. Refrigerate for 5 to 10 minutes or until chocolate is set. Store in airtight container at room temperature for no more than 3 days.