In a mixer with the whisk attachment, beat 2 of the eggs with the sugar on medium speed until pale, fluffy and doubled in volume. Stream in the melted butter and mix until combined.
In a separate bowl, whisk together the flour, baking powder and lemon zest. Switch the mixer to the paddle attachment, and add the flour mixture until fully incorporated. Add the limoncello, pistachios, apricots, and dark chocolate. The mixture will be pretty gooey at this point. Cover it and refrigerate it in the bowl 15-20 mins until firm and more manageable. Preheat the oven to 350.
Divide your dough in two, and roll into logs 1 1/2" wide. Place on a cookie sheet lined with parchment or silpat. Beat the last egg, and egg wash the biscotti logs. Bake 15 mins. Rotate and bake another 15 mins until the dough is golden.
Transfer to a wire rack and cool for 10 mins, or until you can handle the logs. Slice on a deep bias 1/4 - 1/2" thick based on your preference. Place back on the cookie sheet and bake 15 mins, or till the cookies are lightly crispy.
In a double boiler, melt the remaining 1/3 cup of dark chocolate. Dip one end of your cookies in the chocolate, and place on a cookie sheet. I like to sprinkle some flaky salt on the chocolate, but tha'ts optional.