In a medium bowl, whisk together the flour and salt. Set aside. In a large bowl with an electric mixer, or in the bowl of a stand mixer fitted with the paddle attachment, beat butter and cream cheese on medium speed until well blended, about 1 minute.
Add the granulated sugar and beat until smooth, about 1 minute. Add the egg and vanilla and beat on low speed until well combined, about 1 minute. Turn off the mixer and scrape down the bowl with a rubber spatula. Gradually add the flour mixture, mixing on low speed just until blended, about 1 minute.
Using a spatula, scrape the dough into the prepared baking pan and spread it into an even layer. Bake just until the edges are starting to turn light golden brown, and a toothpick inserted in the middle has moist crumbs, 20 to 25 minutes. (Do not overbake! The bars should be quite moist, and almost slightly underbaked in the middle.)
Remove the pan from the oven and set it on a wire rack. Let cool completely. When fully cooled, remove the bars from the pan using the overhanging parchment paper.