Preheat oven to 350°F/180°C.
In a medium bowl, whisk together flour, sugar, baking powder and salt. Using fingers, mix in butter until mixture resembles a coarse meal.
Add egg, milk and extracts. Mix thoroughly until a soft dough forms. Add almonds and apricots.
Divide dough into 3 equal logs, 2-in. wide x 2-in. thick x 14-in. long. Transfer to a parchment paper-lined jelly roll pan. Gently press on the logs so they flatten slightly. Allow space between the biscotti logs as the dough expands during baking.
Brush logs with egg wash and bake in the middle of oven until pale golden and firm, about 20 minutes. Cool on baking sheet on a rack 15 - 20 minutes.
Reduce oven temperature to 300°F/150°C while logs cool.
When the logs are cool enough to handle, carefully transfer baked log to a cutting board. Using a large serrated knife, cut logs diagonally into 3/8-in. wide slices.
Return the cookies to parchment paper-lined sheet and bake in oven for 10 - 12 minutes.
Remove from oven, turn the cookies over and bake until slightly golden, about 5 - 10 minutes more.
Remove from oven and transfer the biscotti to rack. Once cool, store in air tight container.