In a large bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy.
Beat in the pumpkin puree, egg, and vanilla until well combined.
In a separate bowl, whisk together flour, cinnamon, nutmeg, ginger, baking soda, and salt.
Gradually add dry ingredients to the wet mixture, mixing until just combined.
Fold in the rolled oats.
Cover and refrigerate the dough for at least 1 hour.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop 2-tablespoon portions of dough. Flatten slightly, place a caramel in the center, and wrap dough around to fully enclose the caramel.
Place on baking sheets, spacing cookies 2 inches apart.
Bake for 12-14 minutes or until edges are lightly golden and centers are set.
Let cool on the baking sheet for 5 minutes, then transfer to a wire rack.