Preheat the oven to 350°F (180°C). Lightly grease a 9-inch (23-cm) square pan with butter and line it with parchment paper. Set aside.
In the bowl of a stand mixer, use the paddle attachment to cream the butter and sugar at high speed until pale yellow, about one minute.
Scrape down the side of the bowl. Sift in the flour and add the salt. Mix on low speed until the ingredients are incorporated into coarse crumbles.
Dump the shortbread crumbs into the prepared baking pan. Use your hands to spread the crumbs into an even layer, then press down to pack the crumbs into a compact layer. Place the tin in the preheated oven and bake for 22 to 24 minutes or until the edges are golden.
While the crust is baking, make the pumpkin filling. Place the pumpkin purée, sweetened condensed milk, eggs, pumpkin pie spice, salt, and vanilla in the same mixing bowl (don't worry about washing it out). Switch to the whisk attachment.
Mix the pumpkin filling on high speed until creamy and smooth, stopping to scrape down the sides of the bowl halfway through mixing.
Remove the shortbread crust from the oven. Pour the pumpkin filling over the hot crust. Use a spatula to smooth the filling, ensuring it's even in all four corners.
Return the pan to the oven and continue to bake for 35 to 37 minutes, or until the middle is set and no longer wobbly.
Cool the bars in the pan on a wire rack before slicing and serving.
Notes
Leave a parchment paper overhang on all four sides of the baking tin for easy removal.
Cool the bars completely before slicing.
Storage
Store the bars in an airtight container in the refrigerator for up to 5 days. They can also be frozen for up to 2 months. Thaw for an hour or two in the fridge before serving.