Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats and set aside.

In a large mixing bowl, cream the softened unsalted butter with the brown sugar and 1/2 cup granulated sugar until light and slightly fluffy, about 2 to 3 minutes with a hand mixer or 4 minutes with a stand mixer.

Add the egg, vanilla extract and molasses (if using) and mix until fully incorporated and smooth. Scrape down the bowl as needed.

Stir in the pumpkin puree until the mixture is even in color and texture.

In a separate bowl, whisk together the all-purpose flour, cornstarch, baking powder, baking soda, pumpkin pie spice, ground cinnamon and fine salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed or stirring with a sturdy spatula until just combined. Do not overmix; the dough should be soft and slightly sticky.

Cover the bowl and refrigerate the dough for at least 30 minutes, up to 2 hours.

Combine 1/4 cup granulated sugar with 1/2 teaspoon ground cinnamon in a shallow bowl or plate for rolling.

Using a cookie scoop or tablespoon, portion the chilled dough into 1 1/2 tablespoon-sized balls (about 18–20 cookies per batch). Roll each ball lightly between your palms, then roll in the cinnamon-sugar mixture to coat evenly. Place the coated dough balls about 2 inches apart on the prepared baking sheets.

Bake the cookies for 10 to 12 minutes, rotating the pans halfway if your oven has hot spots. The cookies are done when the edges are set and the center still looks slightly glossy and soft—the tops will have small cracks.

Remove the baking sheets from the oven and let the cookies cool on the pan for 5 minutes, then transfer them to a wire rack to cool completely. They will continue to set as they cool.

Repeat with the remaining dough, allowing the baking sheets to cool down between batches if necessary. Store cooled cookies in an airtight container at room temperature for up to 4 days, or freeze for longer storage.