Cream together butter and sugar until fluffy. Add egg and vanilla and mix well.
In another bowl, whisk together flour, pudding mix, baking powder, 2 teaspoons cinnamon, and salt. Add dry ingredients to wet ingredients and mix until dough comes together. Cover and chill at least 1 hour.
In a small bowl whisk together the 1/4 cup sugar and 1 teaspoon cinnamon. Roll about 4 tablespoons of dough into a ball. Break the ball in half, place a caramel into the center of one half, then press the two halves back together to cover the caramel and roll into a ball again. Roll ball in the cinnamon-sugar mixture, then place on a lightly greased baking sheet. Repeat with remaining dough and caramels.
Bake at 350 degrees for 10-12 minutes. Allow to cool for 10 minutes on the baking sheet before transferring to a cooling rack. Store in airtight container. Serve at room temperature or heat the cookies in the microwave for 5-8 seconds before serving to make the caramel extra gooey.