In a large mixing bowl, whisk together the flour, salt, and baking powder until well combined. Set aside.

In another bowl, beat the eggs until light and frothy. Gradually add olive oil, sugar, and vanilla extract, mixing until smooth.

Slowly pour half of the dry mixture into the wet ingredients and fold gently. Gradually add remaining dry ingredients along with anise seeds, sesame seeds, dried apricots, and pistachios until just combined.

Shape the dough into two logs on a floured surface, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper. Remove logs from refrigerator, brush tops with egg white, and bake for 25-30 minutes until golden brown.

Let logs cool for 10 minutes, then slice each log diagonally into 1-inch thick pieces. Arrange cut-side down on baking sheet and bake for an additional 15-20 minutes until crispy.

Transfer biscotti to a wire rack to cool completely before storing in an airtight container.