Prep the pumpkin: Measure the pumpkin puree, then blot it with paper towels to remove excess moisture until you have about 1/2 cup very thick puree. This step keeps the cookies from turning cakey.

Mix dry ingredients: In a medium bowl, whisk flour, cornstarch, baking soda, salt, cinnamon, ginger, and nutmeg. Set aside.

Whisk wet ingredients: In a large bowl, whisk the melted butter, brown sugar, and granulated sugar until glossy and combined, about 30 seconds. Whisk in the egg yolk, vanilla, and the blotted pumpkin puree until smooth.

Combine: Add the dry ingredients to the wet mixture and fold with a spatula just until no dry streaks remain. If using chocolate chips or nuts, fold them in now. The dough will be soft but not runny.

Chill: Cover and refrigerate the dough for at least 45–60 minutes, or up to 24 hours. Chilled dough prevents spreading and keeps the centers soft.

Prep caramels: If the candies are large, cut them in half. For each cookie, plan on one half to one whole soft caramel, depending on size.

Preheat and line: Heat oven to 350°F (175°C). Line two baking sheets with parchment paper.

Form cookies: Scoop 2-tablespoon portions of dough. Flatten slightly in your palm, place a caramel piece in the center, and wrap the dough around it to seal. Roll into a ball and place on the baking sheet, spacing about 2 inches apart.

Bake: Bake 10–12 minutes, until edges are set and centers look slightly underdone. The tops may crack—that’s good. If caramel oozes a bit, nudge it back with a spoon while warm.

Finish: Immediately sprinkle with a pinch of flaky sea salt, if using. Let cookies cool on the sheet for 10 minutes, then transfer to a rack. They’ll firm up as they cool but stay soft inside.