Heat oven to 350° F. Line a baking sheet with parchment. On a rimmed baking sheet, toast the hazelnuts in the oven, tossing occasionally, until fragrant, 10 to 12 minutes. Let cool slightly, then rub in a clean dish towel to remove the skins (discard).
In a large bowl, whisk together the flour, baking soda, baking powder, and salt; set aside.
Using an electric mixer, beat the eggs and sugar on medium-high until light and fluffy, 4 to 5 minutes. Beat in the almond extract.
Gradually add the flour mixture, mixing by hand until just combined (do not overmix). Fold in the hazelnuts, dried cherries, and chocolate.
Shape the dough into two 2-by-10-inch logs and place 3 inches apart on the prepared baking sheet. Bake until golden and firm, 25 to 30 minutes.
When the logs are cool enough to handle, using a serrated knife, slice each log into ⅜-inch-thick slices. Place the slices cut-side down on 2 baking sheets.
Bake, rotating the baking sheets and turning the biscotti over halfway through, until dry and firm, 8 to 10 minutes. Let cool completely on the baking sheets.