In a large mixing bowl, beat the softened butter and powdered sugar with an electric mixer on medium speed for approximately 2 minutes, until smooth and creamy. Add the egg yolk and vanilla extract. Beat briefly until incorporated, scraping down the sides of the bowl as needed.

Add the all-purpose flour and fine salt to the butter mixture. Mix on low speed just until the dough forms soft, cohesive clumps. It should hold together when pressed between your fingers without feeling excessively sticky. Avoid overmixing, which can make the baked crusts tough.

Lightly grease all 24 cavities of a nonstick mini muffin pan with the vegetable oil. Divide the dough into 24 equal portions, approximately 1 tablespoon each. Roll each portion into a ball and place it in a prepared muffin cavity. Press the dough gently across the bottom and up the sides to create a small cup. Keep the thickness as even as possible, with a slight indentation in the center and enough space for the pumpkin filling.

Refrigerate the prepared muffin pan for 20 minutes. The dough should become noticeably firm. This helps prevent the butter from melting too quickly and reduces excessive spreading during baking. While the crusts chill, prepare the pumpkin filling and preheat the oven.

In a medium bowl, whisk together the pumpkin puree, brown sugar, egg, heavy cream, pumpkin pie spice, vanilla extract, and fine salt. Continue whisking until the mixture is completely smooth and evenly blended. The filling should be creamy and pourable, with no visible streaks of egg or clumps of brown sugar.

Preheat the oven to 350°F (175°C) and position a rack in the center. Remove the chilled cookie crusts from the refrigerator immediately before baking. Check that each crust still has a clear indentation for the filling.

Place the mini muffin pan on the center oven rack and bake for approximately 8 minutes. The crusts should look set around the edges but remain pale rather than deeply golden. If the centers puff slightly, carefully press the indentations back into shape with the rounded end of a wooden spoon while the dough is still warm. Leave the oven on.

Carefully spoon approximately 2–2½ teaspoons of pumpkin filling into each prebaked cookie crust. Distribute the filling evenly among the 24 cavities, stopping just below the top edge of each crust. Avoid overfilling, since the pumpkin custard will puff slightly during baking.

Return the muffin pan to the oven and bake for another 14–17 minutes. The cookie edges should be lightly golden, and the pumpkin filling should look set around the edges with only a slight movement in the center. For food safety, the center of the pumpkin custard should reach at least 160°F (71°C). If the filling still looks liquid, bake for another 2–3 minutes and check again.

Remove the muffin pan from the oven and place it on a wire cooling rack. Let the cookies cool in the pan for 15 minutes. The pumpkin filling will continue to firm up as it cools. Avoid removing them immediately, since the warm crusts will be delicate.

Gently run a small, thin knife around the edges of any cookies that appear attached to the pan. Carefully lift the cookies out and transfer them to a wire rack. Allow them to cool for another 30 minutes. The crusts should feel firm enough to handle, and the filling should no longer be warm.

Arrange the cooled cookies in a single layer in an airtight container or on a covered tray. Refrigerate for at least 45 minutes to allow the pumpkin filling to set completely. The finished cookies should have a tender, buttery crust and a smooth filling that holds its shape when bitten.

Just before serving, top each cookie with a small spoonful or swirl of the optional whipped cream. Finish with a light dusting of the optional ground cinnamon. Serve the Pumpkin Pie Cookies chilled or slightly cool. Keep any remaining cookies refrigerated.