Make the topping by mixing the sugar and cinnamon together. Set aside.
Cream the butter and sugar together until fluffy (1-2 minutes) with an electric mixer. Mix in the egg and vanilla for another 2-3 minutes and then set aside.
In another bowl, whisk together the flour, cream of tartar, baking soda, cinnamon and salt. Slowly add the dry ingredients to the wet ingredients and mix together on low until well combined.
Gently fold in the peaches.
Take 1-2 Tbsp of dough (depending on how big you want to make the cookies) and roll into a ball. Roll the dough balls in the topping mixture and place on a greased cookie sheet. Bake for 10 minutes and then cool for about 10 minutes on the cookie sheet before transferring to a wire rack to cool completely.