Heat the oven to 350°F and grease a 9x13-inch baking dish with butter or nonstick spray. Coat the bottom and corners well so the finished cake releases cleanly.

Prepare the vanilla cake batter as directed on the box, pour it into the dish, and bake for about 20 minutes. Check the center with a toothpick, and remove the cake when the tester comes out clean.

Let the baked cake cool slightly before moving on. The crumb should feel set on top instead of soft and steamy, which helps it take in filling without turning gummy.

Whisk the sweetened condensed milk, melted butter, brown sugar, cinnamon, and salt in a clean bowl. Keep whisking until the mixture looks smooth and the sugar no longer feels grainy.

Beat the softened cream cheese and butter with an electric mixer until completely smooth. The mixture should look creamy and uniform, with no visible cream cheese specks.

Mix in the powdered sugar gradually on low speed, then add the vanilla, salt, and 1 tablespoon heavy cream before beating on high. Stop when the frosting looks light and fluffy, adding the remaining tablespoon of cream only if you want a softer spread.

Use a wooden spoon handle to poke holes across the cake, stopping about 80 percent of the way down, then pour on the filling and press it into the holes with a rubber spatula. The filling should settle into the channels without flowing around the cake’s edges or pooling at the bottom.

Wait until the filling has soaked in, then spread the cream cheese frosting evenly over the surface and chill for 30 minutes before slicing. The cake should feel cool to the touch, and the chilled frosting will hold neat edges when cut.