In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter, granulated sugar, and brown sugar together on medium-high speed until light and fluffy, about 3 minutes.

Add the egg and vanilla paste or extract and beat until combined. Add the pumpkin puree and mix until incorporated, scraping down the sides and bottom of the bowl as needed.

In a separate bowl, whisk together the flour, pumpkin pie spice, baking soda, baking powder, and salt.

Add the dry ingredients to the wet ingredients and beat on low speed just until combined. The cookie dough will be thick and soft.

Cover the dough and chill in the refrigerator for 2 hours.

Preheat the oven to 350°F (177°C). Line 2 large baking sheets with parchment paper. Scoop chilled dough with a small cookie scoop into approximately 1 1/2 tablespoon portions. Arrange 2 inches apart on the prepared baking sheets.

Bake for 15-17 minutes. Remove the cookies from the oven and lightly press one marshmallow into the center of each cookie.

Return to the oven and bake for another 3–4 minutes, until the marshmallows are soft and puffed. Remove from the oven and gently press each marshmallow down to slightly flatten them.

Cool the cookies on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Melt the semi-sweet chocolate in a double boiler or microwave in 20-second increments, stirring between each, until completely smooth.

Spoon the melted chocolate over each marshmallow-topped cookie. Allow the chocolate to set at room temperature for 30 minutes until firm.