In a stand mixer with the paddle attachment or in a bowl with a hand mixer, cream together unsalted butter and sugars until the mixture is light and slightly fluffy. Then mix in pumpkin and vanilla and mix to combine.
In a separate bowl, whisk together flour, salt, baking soda, and spices. Slowly add that to the mixing bowl until just mixed together. Try not to overwork dough.
Preheat oven to 350 degrees F. Make cookies by rolling a heaping tablespoon-sized ball of dough in your hands and then rolling it in sugar. Place it on a baking sheet and press down on the dough ball with a ¼ cup measuring cup to flatten it. Repeat with all the cookies. Don’t crowd the cookies on the baking sheet. I shoot for 8 cookies per sheet.
TIP: If your measuring cup is sticking to the dough, dip it in sugar.
Bake flattened cookies for 5 minutes. Then, remove them and use the measuring cup to make a divot in each cookie for the filling. You can press down firmly on the cookies at this point. Return to the shaped cookies to the oven for another 6-7 minutes to finish cooking.
When cookies come out of the oven, let cookies cool before filling and frosting them.
For Pumpkin Filling:
Whisk together pumpkin, brown sugar, and spices until smooth.
Once your cookies are cool, either spoon the filling into the cookies or pipe them in with a flat piping tip.
For Cinnamon Icing:
In a stand mixer with the whisk attachment (or by hand), whisk together meringue powder and water until there are no lumps. Then, whisk in the cinnamon and powdered sugar in 1 cup batches.
The icing should turn smooth and flat after about 10 seconds if you drizzle some on itself. Add water to the icing in very small increments (by the drop or with a spray bottle) until you get the right consistency for it. Add orange color after the consistency is right.
Pipe the icing on the cooled and filled cookies to cover the filling. Then, dot with whipped cream before serving.
Cookies keep well in the fridge for a few days, but leave off the whipped cream until right before serving.