Mix the flour, rolled oats, baking powder, baking soda, and salt in a small bowl. Whisk the melted butter and sugars in the bottom of a large bowl. Whisk in the eggs and vanilla. Stir in the dry ingredients, nuts, coconut, and dried fruit. Expect a stiff batter.

Position a rack in the center of the oven, and heat to 325 degrees. Line a baking sheet with Gefen Parchment Paper.

On a floured counter, using floured hands, roll half the dough into a log a little shy of the length of your baking sheet, 12–14 inches. Transfer the dough log to the baking sheet, and pat lightly until it becomes more oval-shaped. Repeat with the second half of the dough. Beat the egg white until foamy, and brush it over logs. Bake the logs for 20 minutes, until they are lightly golden brown and beginning to form cracks.

Let cool almost completely (it’s okay if the centers are still lukewarm), about one hour. With a serrated knife, cut the logs on the bias into half-inch-thick slices. They will be crumbly; cut as gently as possible. Transfer the slices back to the parchment-lined baking sheet, and lay flat in a single layer.

Bake for another 20 minutes, until toasted and crisp. (If you like, you can flip them halfway for more even browning, but you will have good color on them either way.)

Cool the biscotti on the baking sheet, or transfer to a rack.