Preheat your oven to 350°F (175°C). Spread the almonds on a baking sheet and toast for 8-10 minutes, until fragrant. Let them cool completely, then set the oven temperature to 350°F (175°C) if you changed it.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, whisk the melted butter and sugar. Add the eggs one at a time, followed by the vanilla and almond extracts, whisking well after each addition until smooth.
Pour the dry ingredients into the wet ingredients and mix with a spoon until just combined. Fold in the cooled, toasted almonds. The dough will be sticky.
Line a large baking sheet with parchment paper. Divide the dough in half and shape each half into a log about 10 inches long and 2 inches wide. Place the logs several inches apart on the baking sheet.
Bake for 25 minutes, or until the logs are firm and lightly golden. Remove from the oven and let them cool on the baking sheet for at least 1 hour. This cooling step is important for clean slicing.
Reduce the oven temperature to 300°F (150°C). Carefully transfer a cooled log to a cutting board. Using a sharp serrated knife, slice the log diagonally into 1/3-inch thick cookies.
Arrange the slices cut-side down on one or two parchment-lined baking sheets. Bake for 12 minutes, then remove the sheets from the oven, flip each cookie over, and bake for another 10-12 minutes, until they are dry and golden.
Let the biscotti cool completely on the baking sheets. They will become crisp as they cool.