Place pumpkin puree in the middle of a kitchen towel. Gather up edges of kitchen towel and gently squeeze pumpkin over a sink or bowl until all the liquid is squeezed out. Set pumpkin aside.
Place butter and sugars in the bowl of a large stand mixer, fitted with a paddle attachment OR in a large mixing bowl with a wooden spoon. Mix on medium speed or by hand until creamy, about 2 minutes.
Beat pumpkin, vanilla, oats, flour, pumpkin pie spice, and salt into butter mixture until dough is just combined. Wrap dough in plastic wrap and chill 2 hours or up to 6 days.
Preheat oven to 350F and line a square 8-inch with parchment paper. Remove dough from refrigerator and pat in an even layer in pan. Prick dough all over with a fork.
Bake shortbread at 350F 25-30 minutes until a light golden brown. Allow shortbread to cool completely on a wire cooling rack.
Salted Caramel
Place sugar in a medium saucepan over medium heat and allow to melt. Once melted, whisk in butter and bring to a boil. Slowly add cream (carefully, it will splatter) whisking constantly and allow caramel to cook until golden brown and bubbly, about 3-5 minutes. Remove caramel from heat and mix in salt.
Immediately pour caramel over cooled shortbread. Allow to set 10 minutes before slicing into bars and topping with additional flaky sea salt. Enjoy!
Notes
Storing InstructionsStore bars in an airtight container at room temperature up to 4 days.