Preheat the oven to 325°F. Line two large baking sheets with parchment paper and set them aside.
In a large bowl, whisk together the flour, baking soda, and salt. Set it aside.
In a stand mixer bowl with the paddle attachment, or in a large bowl with a handheld mixer, combine the butter and both sugars. Beat on medium speed for about 3 minutes. The mixture should be light and fluffy. Scrape down the bottom and sides of the bowl as needed.
Beat in the vanilla and almond extract.
Lower the mixer speed to medium-low. Add the eggs one at a time. Beat well after each egg. Scrape down the sides and bottom of the bowl as needed.
Reduce the mixer speed to low and add the flour mixture, beating until just combined. Mix in the chocolate chips, pistachios, and cherries, just until evenly combined.
You can bake right away. Or, you can cover the dough and refrigerate it for up to 1 hour. Do not refrigerate it longer, or the dough will get too hard to scoop.
Using a large spring-loaded cookie scoop, scoop heaping 3 tablespoon-sized mounds (80g) of cookie dough and roll them into a ball. Place the dough ball on the prepared sheet. Repeat this process with all the dough, leaving 2 inches of space between each cookie.
Bake one sheet at a time for 12 to 13 minutes, or until golden on the edges but still soft in the center.
Take the cookies out of the oven. Use a spatula to gently tuck in any edges that spread too much while baking. This will help make a perfectly round cookie.
Press extra chocolate chips, cherries, and pistachios on top, if desired. Cool cookies on the baking sheet for 20 minutes before placing them on a wire rack to serve or move.