Preheat the oven to 350°F. Line an 8x8 baking pan with parchment paper, and set aside.
In a medium bowl, beat the butter and sugar until light and fluffy. Add the canned pumpkin, and beat until smooth.
Stir in the flour, salt, and pumpkin pie spice until it's just mixed. Don't overbeat the dough! A little crumbly is fine.
Drop the dough into the prepared 8x8 pan, and press firmly with your hands until it's even and packed. I use the bottom of a measuring cup to get it as level as possible.
Bake for about 20-25 minutes, until the shortbread is a light golden brown. Let it cool for about 15 minutes while you make your caramel.