Preheat oven to 350°F. Line a baking sheet with parchment paper and set it aside.
In a large mixing bowl (or stand mixer), cream together the butter, oil, granulated sugar, and powdered sugar until smooth and fluffy.
Mix in the egg and vanilla extract until everything is fully combined.
Stir in the flour, salt, and baking powder until the dough just comes together.
Using a large cookie scoop, portion out 9 equal balls of dough onto your prepared baking sheet. Gently flatten each ball to about 1-inch thick. Then, using the back of a spoon, press down in the center to make a little well for the pumpkin filling.
Bake for 8–9 minutes, until the edges are set. Let the cookies cool on the baking sheet while you prepare the filling.
In a medium bowl, beat the cream cheese and brown sugar until smooth. Mix in the pumpkin puree, pumpkin pie spice, and a few drops of orange gel food coloring.
In another medium bowl, whip the cold heavy cream with the white sugar and vanilla extract until stiff peaks form.
Gently fold the whipped cream into the pumpkin mixture until fully combined. Transfer the mixture to a piping bag fitted with a large tip.
Pipe a generous dollop of pumpkin filling into the center of each cookie. Pick up each cookie carefully and tap it lightly on the counter to help the filling spread just a little.
Add an extra swirl of whipped cream on top.