Preheat the oven to 350°F and line a baking sheet with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment (or a large bowl with a hand mixer), beat together the butter, sugar, and brown sugar until smooth. Add in the eggs, vanilla, and almond extract and beat until just combined.
Add in the flour, baking powder, and salt and mix until fully incorporated. Then stir in the toasted hazelnuts. The dough should be sticky.
Scoop half the dough onto one side of baking sheet and pat it into a 10 inch x 2 inch rectangle that’s about 1 inch thick (lightly wetting your hands helps a lot with this step). Repeat with the other half of the dough.
Bake for 20 to 30 minutes, until golden brown all over. Remove from the oven and let cool for 25 to 30 minutes. Reduce the oven temperature to 325°F.
Carefully transfer the logs to a cutting board and use a spray bottle filled with room-temperature water to very lightly spritz them. Wait about 5 minutes before using a very sharp serrated knife to slice biscotti ½ inch wide.
Return the slices to the baking sheet, standing them up with ½ inch in between them, so air can circulate around them. Bake for another 25 to 30 minutes, until dry and golden. Remove from the oven and transfer to a wire rack to cool.
Dip in the melted chocolate and sprinkle with chopped hazelnuts and flaky sea salt.
Store in an airtight container at room temperature for up to 2 weeks!