In a mixing bowl, sift the cake mix to remove any lumps. Add the instant vanilla pudding mix, sour cream, brown sugar, flour, eggs, pineapple juice, vegetable oil, and vanilla extract.
Mix all the ingredients on medium speed for about a minute. Make sure to scrape down the sides of the bowl to fully incorporate everything, then mix for an additional minute to achieve a smooth, lump-free batter.
Carefully pour the batter over the brown sugar, pineapple rings, and cherries in the pan, making sure everything is evenly covered.
Place the pan in the preheated oven and bake for 40-45 minutes. You'll know the cake is done when it springs back when lightly touched, and a toothpick inserted into the center comes out clean or with a few crumbs attached. If your cake seems to brown too quickly, you can cover it loosely with foil during the last few minutes of baking.
Once the cake is finished, allow it to cool in the pan for about 10 minutes. If the cake has a dome in the center, gently press it down with a clean towel or carefully trim it with a serrated knife for an even surface.
For the flip, place your cake platter on top of the sheet pan and, using dish towels or oven mitts to protect your hands, flip the cake upside down onto the platter. Let the cake pan sit upside down for a couple of minutes, allowing the brown sugar glaze to fully coat the cake.
Serve warm for the best texture and flavor. If you're not serving immediately, refrigerate the cake and take it out a few hours before serving to let it return to room temperature. The cake tastes best at room temperature or slightly warm, as cold temperatures can affect the texture due to the butter in the recipe.