Combine the ¼ cup granulated sugar and 1 teaspoon cinnamon in a small bowl. Stir until the cinnamon is distributed evenly, then place the coating mixture aside for later use.
Add the softened butter and 1⅓ cups granulated sugar to a large mixing bowl. Using an electric mixer, beat the ingredients for 1–2 minutes, or until the mixture becomes pale, airy, and fluffy.
Mix the egg and vanilla extract into the creamed butter mixture. Continue beating until the wet ingredients are thoroughly incorporated, then set the bowl aside.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, 2 teaspoons cinnamon, and salt until uniformly blended.
Gradually add the dry mixture to the prepared wet ingredients. Mix on low speed only until a cohesive cookie dough forms, taking care not to overmix.
Gently fold the peeled, finely diced apple into the dough until the pieces are evenly dispersed.
Portion the dough with a cookie scoop, then lightly flatten each serving between your fingers.
Press one soft caramel into a slightly flattened shape and position it in the center of each portion of dough.
Carefully draw the dough around the caramel, fully enclosing it so no part of the candy remains exposed. Roll the sealed dough gently between your palms to form a smooth ball.
Roll each filled dough ball through the reserved cinnamon-sugar mixture until the exterior is completely coated.
Place the coated dough balls on a greased baking sheet, leaving approximately 2 inches of space between each cookie.
Bake at 350°F (175°C) for 10–11 minutes, or until the cookies show only a very light golden color.
Leave the cookies on the baking sheet for at least 15–20 minutes before transferring them to a wire cooling rack. This resting period allows the caramel and cookie structure to set properly.