Heat your oven to 350 degrees F. Place your chopped hazelnuts on a rimmed baking sheet and bake them for 10 minutes, stirring at the halfway point. Let the nuts cool on a wire rack.
If your butter is not softened, heat it in the microwave on defrost for four seconds at a time. In a large mixing bowl, add your softened butter, eggs, sugar, liqueur, and vanilla and beat on medium until blended.
In a medium bowl, whisk your flour, baking powder and salt. Add the flour mixture to your egg mixture and stir it in. Stir in the toasted hazelnuts. Blend it as best as you can with a spoon.
On a floured surface, scrape out your dough. With floured hands and adding a little extra flour as needed, knead the dough for a minute or so, until it comes together nicely. (If the dough is sticky and not holding together, you need to add a little more flour.)
Divide the dough into two equal parts. Shape each section of dough into a log about 10 inches long and two inches wide. (See photos in the post.)
Bake the dough logs on a greased baking sheet or one lined with parchment paper for 20-25 minutes. You don't want to brown the dough.
Remove the dough logs from the oven and let them cool in the pan for 10 minutes. Keep the oven on, since you will need it again.
After 10 minutes, slice the dough logs on the diagonal, starting at one corner. (See photos.) Continue slicing the logs diagonally into strips 1 inch wide.
Arrange the slices with the cut side facing up on your baking sheet (they brown more nicely if you don't use parchment). No grease is needed on the pan. Bake the first side for 9 minutes, then flip over the biscotti and bake the second side for 9 minutes.
Cool the biscotti on a wire rack.
For the chocolate dip, place your dark chocolate chips in a small, microwaveable bowl and lightly cover it with wax paper. Heat in the microwave on high for 20 seconds at a time until the chocolate begins melting. Stir and heat some more if needed, until your chocolate is melted.
Repeat with another small bowl and your white chocolate chips.
Your biscotti should be cool enough to touch. Dip the flat bottom of each cookie in either the white or dark chocolate. (I do half a batch of white and half a batch of dark chocolate.)
Let the biscotti dry on a wire rack until the chocolate hardens.
Store them in a covered plastic container at room temperature. Enjoy the biscotti dunked in your coffee, hot chocolate or cold milk. (You can eat them without dunking them, but they'll be a bit dry.)
If you don't wish to use the hazelnut liqueur, you can substitute a teaspoon or two of almond extract.