Whisk together the flour, cream of tartar, baking soda, and salt in a medium bowl and set aside. In a separate small bowl, mix 1/4 cup of the granulated sugar with the cinnamon and set that aside too. This is your rolling mixture.

In a large bowl, beat the softened butter and the remaining 1 1/4 cups granulated sugar together with a mixer on medium speed for about 3 minutes until the mixture is pale and fluffy. Scrape down the sides.

Add the eggs one at a time, beating for 30 seconds after each one. Mix in the vanilla extract. Add the flour mixture and mix on low just until the dough comes together. Do not overmix.

Scoop about 1 1/2 tablespoons of dough and flatten it into a disc in your palm. Press one soft caramel square into the center, then wrap the dough up around it and roll into a ball, making sure the caramel is fully sealed inside. If dough cracks, press it back together. Repeat with all the dough.

Roll each stuffed dough ball in the cinnamon sugar mixture until evenly coated, then place them on a parchment-lined baking sheet about 2 inches apart. Refrigerate the trays for at least 15 minutes. This step keeps the cookies from spreading too flat.

Preheat your oven to 375 degrees F while the dough chills. Bake one sheet at a time for 10 to 11 minutes until the edges are set and the tops look just barely done. The centers will look slightly underdone and that is exactly right. They firm up as they cool.

Let the cookies cool on the baking sheet for 5 minutes before moving them to a wire rack. The caramel inside will be very hot right out of the oven. Give them at least 10 minutes before eating so no one burns the roof of their mouth.