Preheat the oven to 350 degrees. Spray a 13- by 9-inch baking pan with cooking spray and set aside.

Combine the cake mix, pudding, eggs, milk, and oil in a large mixing bowl. Beat with an electric mixer until smooth, scraping the sides and bottom of the bowl as necessary.

Pour into the prepared pan, smooth the top, and bake 32 to 42 minutes, until a toothpick inserted into the center of the cake comes out clean.

While the cake is in the oven, combine the pineapple WITH JUICES and sugar in a small saucepan set over medium heat. Bring to a boil, stirring often. Boil for 3 minutes, still stirring.

Set aside while the cake finishes baking.

Set the baked cake on a wire rack to cool for 5 minutes. Use a long-tined fork to poke holes all over the cake, going about 3/4 of the way down into the cake. (If you don’t have a long-tined fork you can use a toothpick and swirl it around to make the holes a little bigger.)

Pour the pineapple over the top of the still-hot cake and use a rubber spatula to spread it around evenly (do this gently).

Cool completely before making the frosting.

Combine the cream cheese and butter in a medium bowl. Beat with an electric mixer on medium until smooth.

Gradually beat in the powdered sugar to combine. Add the vanilla and salt and beat on medium speed until frosting is smooth and fluffy.

Dollop the frosting over the cooled cake and use a small offset spatula to spread it out gently. Slice and serve.

Uneaten cake can be stored, covered, in the fridge for up to 4 days or in the freezer, tightly wrapped, for up to 2 months.