1. Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
2. In a large mixing bowl, stir together the flour, sugar, baking soda, salt, semisweet chocolate chips, white chocolate chips and coconut.
In a smaller bowl, beat together the vanilla extract, eggs and egg white until well combined.
3. Pour the egg mixture into the dry ingredients and stir until it's mostly combined.
The dough will be crumbly and not come together at all.
4. Turn out onto a floured board and knead the dough with floured hands until it forms a mostly smooth ball.
5. Place the dough onto the prepared baking sheet and pat into a 1-inch thick piece, pushing the ends in until the dough is rectangular in shape.
6. Bake for 30-35 minutes, until golden at the edges. Remove from the oven and transfer the log to a cutting board.
Cut the biscotti into 1/2 inch slices (it helps to score it with a serrated knife and then cut with an extra-sharp knife straight down). Place the slices on a parchment lined baking sheet. It's okay if they touch.
7. Bake for 10 minutes. Flip all the slices and then bake for another 10 minutes. Let cool on the baking sheet for five minutes, then transfer to a wire rack to fully cool. The biscotti hardens as it cools.
8. Store in an airtight container for up to one week.