Preheat the oven to 300 degrees F. Line a sheet pan with parchment paper.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, brown sugar, granulated sugar and cinnamon on medium speed for 3 minutes, until light and fluffy. With the mixer on low, gradually add the 2 whole eggs, the egg yolk (reserve the egg white), and vanilla and mix until combined, scraping down the bowl with a rubber spatula.
In a medium bowl, combine the all-purpose flour, almond meal, baking powder and salt. With the mixer on low, slowly add the dry mixture to the butter-sugar mixture, mixing only until combined. Scrape down the bowl and beater and make sure all the ingredients are combined. Stir in the pistachios and cherries.
Roll the dough into a ball on a well-floured board and cut in half. With floured hands, roll each piece into a cylinder about 11 inches long by 2 inches in diameter and place them 3 inches apart on the prepared sheet pan.
Place the reserved egg white in a bowl and beat with a whisk for 15 seconds. Brush the logs with the egg white (save the rest!) and sprinkle each with 1 teaspoon of turbinado sugar. Bake for 45 minutes, until lightly browned (the logs will be soft). Cool for 30 minutes.
Turn the oven down to 275 degrees F. Line two sheet pans with parchment paper. With a serrated knife, slice the biscotti 1/2 inch thick at a full 45-degree angle. Place the slices cut-side up on the prepared sheet pans. Brush them with the egg white and sprinkle generously with turbinado sugar. Bake for 45 to 50 minutes, turning each slice once, until browned and fully baked. Transfer to a baking rack to cool.