Combine brown sugar, 1/2 cup butter, and sweet vermouth in a saucepan over low heat; cook and stir until sugar is dissolved, about 5 minutes.
Arrange cherries and spoon pineapple into the bottom of a 9x13-inch baking dish. Pour brown sugar mixture over fruit.
Beat eggs in a bowl using an electric mixer on medium-low speed until smooth. Add 1/2 cup melted butter, pineapple juice, vanilla extract, and star anise to eggs; beat on medium-low speed until well combined, about 1 minute. Gradually add cake mix, about 1/2 cup at a time, to egg mixture, scraping sides of bowl with a spatula until batter is smooth and fluffy. Pour batter over fruit mixture until evenly spread in dish.
Bake in the preheated oven until cake is golden brown and completely set in the middle, about 1 hour. Cool cake for 15 minutes in the dish. Run a knife along the edge of the cake to loosen. Place a platter over the cake and flip cake onto platter.
I always use canned dark and sweet cherries rather than maraschino, because maraschino cherries have a nasty chemical "flavor" that covers up the pineapple, IMHO.
I also prefer Bob's Red Mill® cake mixes because the resulting cake has more heft to it, without tasting gritty or dry. Therefore, you can use BRM mixes for recipes with frosting or fruit, and you can add little touches such as vanilla or fruit juice, and the cake will still hold together. However, if you're going to use a BRM mix for something like this recipe, it's best to 1) turn down the heat to 325 degrees F (163 degrees C) and let the cake set up slowly, 2) use butter instead of oil so the cake batter has even more moisture in it, and 3) use a 9x13-inch glass pan.
Per Serving: 524 calories;20 g fat;
82.4 g carbohydrates;
2.6 g protein;
105 mg cholesterol;
450 mg sodium.