In a medium bowl, whisk flour, baking soda, baking powder, and salt together. Set aside.

In the bowl of a stand mixer fitted with a paddle attachment, cream butter, white sugar, and brown sugar together until very light and fluffy, about 5 minutes. You can also use a hand mixer and mix together in a large bowl.

Add eggs, one at a time, mixing well after each addition. Stir in the vanilla and almond extract. Be sure to scrape down the bowl as needed.

Reduce speed to low, add dry ingredients, and mix until just combined, 5 to 10 seconds. Stir in cherries and chocolate pieces gently.

Cover mixing bowl and refrigerate for 24 hours, up to 72 hours.

When ready to bake, preheat oven to 350? (180?). Line a baking sheet with parchment paper or a nonstick baking mat.

Take the dough out and let it sit at room temperature to soften before scooping. Scoop into 1-inch balls (about 1 1/2 tablespoons) and place about 2 inches apart onto your cookie sheet.

Bake until golden brown but still soft, 10-12 minutes. Edges should be set, and the top is golden brown; the middle may still look slightly underdone. Transfer sheet to a wire rack for 10 minutes, then slip cookies onto another rack to cool a bit more.