Prep Your Peaches: If using fresh, peel, pit, and very finely dice your peaches. You want the pieces small enough that they distribute well throughout the dough without making it too lumpy or wet. If using frozen, make sure they are fully thawed and drain off all excess liquid before dicing finely.
Cream the Good Stuff: In a large bowl, or the bowl of your stand mixer, cream together the Crisco shortening and 2 cups of granulated sugar until the mixture is light and fluffy. This can take a couple of minutes.
Add Wet Ingredients: Beat in the room temperature eggs one at a time, mixing well after each addition. Stir in the vanilla extract and the 2% milk.
Combine Dry Ingredients: In a separate medium bowl, whisk together the flour, baking soda, 2 teaspoons of cinnamon, cream of tartar, and salt.
Combine Wet and Dry: Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined. Be careful not to overmix!
Fold in Peaches: Gently fold the finely diced peaches into the dough. Distribute them as evenly as possible. The dough will be quite soft at this point, which is fine.
Chill the Dough: Cover the bowl and refrigerate the dough for at least 30 minutes (or up to 2-3 days). Chilling helps the dough firm up, makes it easier to roll, and prevents the cookies from spreading too much in the oven.
Preheat and Prep: While the dough chills, preheat your oven to 375°F (190°C). Line baking sheets with parchment paper.
Make the Coating: In a small shallow bowl, whisk together the coating sugar and cinnamon.
Scoop and Roll: Take spoonfuls of the chilled dough (a cookie scoop works perfectly here, about 1.5 to 2 tablespoons per cookie) and roll them into balls.
Coat 'Em Up: Roll each dough ball generously in the cinnamon-sugar coating, making sure it's well covered on all sides.
Place and Bake: Place the coated dough balls about 2 inches apart on the prepared baking sheets. Bake for 8-10 minutes, or until the edges are lightly golden and the centers look just set (they might still look a little soft, that's okay!).
Cool: Let the cookies cool on the baking sheets for a couple of minutes before transferring them to a wire rack to cool completely.
Enjoy!: Grab a warm cookie (if you can wait!), maybe a glass of milk, and savor that peachy, cinnamony goodness!