Let 8 ounces cream cheese sit at room temperature until softened. (Alternatively, place the cream cheese in a small microwave-safe bowl, and microwave in 15-second bursts until very soft, 30 to 60 seconds total.)

Arrange a rack in the middle of the oven and heat the oven to 350°F. Line the bottom and the 2 long sides of a 9x13-inch baking pan with a sheet of parchment paper, making sure it is long enough to hang over the sides by at least 1 inch to form a sling.

Place 1 stick unsalted butter in a medium microwave-safe bowl. Microwave in 20-second bursts until melted, 40 to 60 seconds total. (Alternatively, melt the butter in a small saucepan over medium heat and transfer to a medium bowl.) Let cool slightly.

Add 1 (15.25-ounce) box yellow cake mix and 2 of the large eggs to the melted butter. Beat with an electric hand mixer or in a stand mixer with the paddle attachment on medium speed until smooth, 25 to 30 seconds (the batter will be very thick). Transfer to the baking pan and spread into an even layer.

Wipe out the bowl and paddle (no need to wash). Add the cream cheese, remaining 2 large eggs, 1 pound powdered sugar, and 1 teaspoon vanilla extract. Beat with the mixer on medium-low speed until smooth, scraping down the sides once or twice, 40 to 45 seconds total. Pour over the top of the cake batter and spread it into an even layer.

Bake until golden brown around the edges but the center is slightly jiggly when the pan is gently shaken, 35 to 40 minutes. Place on a wire rack and let cool completely, 2 to 3 hours.

Run a thin knife around the edges of the bars to loosen. Grasping the excess parchment paper, lift the slab out of the pan and place on a cutting board. Cut into 24 pieces.