Prep your tools. Line two baking sheets with parchment paper. Set the oven to 350°F (175°C). If adding nuts, toast them in a dry skillet over medium heat for 3–5 minutes until fragrant, then cool.

Whisk dry ingredients. In a medium bowl, whisk flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon until combined.

Mix wet ingredients. In a large bowl, whisk melted butter, oil, brown sugar, and granulated sugar until smooth. Add the egg yolk and vanilla. Whisk again until glossy. Stir in the pumpkin puree until fully blended.

Combine the dough. Add the dry ingredients to the wet mixture. Use a spatula to fold until no streaks of flour remain. If using chocolate chips or nuts, fold them in now.

Chill the dough. Cover and refrigerate for at least 30 minutes and up to 24 hours. This helps prevent excessive spreading and deepens flavor.

Portion and bake. Scoop heaping tablespoons (about 1 1/2 tablespoons each) and place them 2 inches apart on the prepared sheets. Lightly flatten the tops with your fingers or the bottom of a glass. Sprinkle with coarse sugar if using. Bake for 10–12 minutes, until the edges look set and the centers are slightly puffed. They may seem soft—this is good.

Cool. Let cookies rest on the sheet for 5 minutes, then transfer to a wire rack to cool completely. They will continue to set as they cool.

Make the glaze. Beat cream cheese, butter, and vanilla until smooth. Mix in powdered sugar and a pinch of salt, then add milk a little at a time until pourable but thick. Drizzle over cooled cookies or spread a thin layer on top.

Serve. Enjoy as is, or dust with a pinch of cinnamon for a bakery-style finish.