Heat the oven to 325°F. Put parchment paper on a baking sheet.
In a medium bowl, combine the flour, baking powder, baking soda, and salt. Mix well and set aside.
In a large mixing bowl, combine the olive oil and granulated sugar; mix on high speed (medium-high if using a freestanding mixer); for 3 minutes. Meanwhile, combine the brown sugar and chopped chocolate bar in a food processor; process until the chocolate is very fine. Add to the sugar/oil mixture and continue to beat 2 minutes more; or until well blended. Add the eggs, one at a time, allowing each egg to be fully incorporated before adding the next; add the vanilla (and Frangelico, if using) mix well. Reduce the speed to medium (or low); add the dry ingredients; mix until well blended. Add the nuts, apricots, and chopped Baci. Mix well.
With floured hands (the dough will be sticky) shape the dough into two 10 inch by 2 inch logs. Place the rolls on the parchment paper about 5 inches apart (there is no need to flatten the rolls, they will spread as they cook). Bake 25 - 30 minutes or until a toothpick, when inserted into the center, comes out clean. Remove the pan to a rack and allow to cool for 10 minutes; remove the biscotti loaves from the pan and allow to cool on the rack for 10 minutes more.
Using a serrated knife, cut the loaves diagonally into ½ inch slices. Arrange, cut side down, on an ungreased cookie sheet (you will most likely need 2 sheets to hold the biscotti for the second cooking). Bake 10 minutes; turn and bake 10 minutes more. Cool completely. May be stored at room temperature in an airtight container for up to 10 days. Makes about 2 ½ dozen biscotti