Preheat oven to 350°F. Line a large baking sheet with parchment paper.
Combine the flour, sugar, oats, baking powder, baking soda, and salt in the bowl of a stand mixer.
Blend on low speed for about 30 seconds.
In a separate bowl, whisk together the eggs and then whisk in the vegetable oil, orange zest, lemon zest, vanilla extract, and almond extract.
Mix in the butter and then add the egg mixture. Mix until fully combined.
Fold in the dried cherries and the pistachios.
Transfer dough to a lightly floured surface and divide in half. Using floured hands, shape each dough half into a 12 to 14" long log.
Transfer the logs to the prepared baking sheet, about 5" apart. Flatten each log into a 2" wide strip (about ½" - ¾" tall).
Bake until lightly browned and set, about 25 minutes, rotating the pan about halfway through.
Transfer to a rack and let cool for 15 minutes.
Reduce the oven to 250°F. Line a second baking sheet with parchment paper.
Transfer the biscotti to a work surface. Using a large knife, cut each log diagonally into ⅓"-thick slices.
Arrange slices, cut side down, on the baking sheets. Bake biscotti until crisp, about 40 minutes, rotating halfway through.
Transfer to wire rack to let cool.