Make the cake batter: Combine the flour, granulated sugar, milk, shortening, baking powder, vanilla, salt, eggs, pineapple juice and 4 tablespoons of the butter in a large bowl. Beat with a mixer on medium speed until well combined. (There will still be a few small lumps in the batter.) Set aside.
Melt the remaining 4 tablespoons butter in a 12-inch cast-iron skillet over medium heat; swirl to thoroughly coat the skillet. Sprinkle the brown sugar over the butter, making sure it's evenly distributed--you want the entire surface of the butter to be covered in brown sugar. Do not stir. As soon as the sugar dissolves, remove from the heat, layer the pineapple slices over the top and add cherries to the middle of the pineapple slices. Pour the batter evenly over the pineapple and gently spread to even out the top. Bake until a toothpick inserted into the center of the cake comes out clean, 30 to 40 minutes.
Immediately run a knife around the edge of the cake, then put a plate upside down on top of the skillet. Carefully invert the skillet so the cake is turned onto the plate. It should come out pretty easily; if bits of cake stick to the skillet, use a small knife to patch it together. Let cool slightly before cutting into wedges. It's best served warm, but room temperature is fine too.