Preheat the oven to 350°F and line two baking sheets with parchment paper.
Cream the butter, sugar, and brown sugar in a stand mixer until smooth.
Beat in the egg, pumpkin puree, and vanilla until the mixture looks fluffy and smells amazing.
Add the flour, salt, baking powder, pumpkin pie spice, and cinnamon. Mix until just combined. Don’t overmix or your cookies won’t stay soft.
Scoop big, bakery-style mounds of dough with an ice cream scoop and drop them on your sheets, leaving space for spreading. About ¼ cup or a bit less.
Bake for 10–12 minutes, until the edges are just turning golden brown. These cookies should be soft, not crispy.
Cool completely on a wire rack.
Beat the butter and cream cheese together until silky smooth then add the caramel sauce, vanilla, and powdered sugar. Mix on low until combined, then on medium for a couple of minutes until fluffy enough to spoon straight from the bowl.
Pipe the frosting in a spiral over each cooled cookie with a piping bag and large round tip.
Dust lightly with pumpkin pie spice for that bakery-finished look.