Preheat the oven to 325°F. Grease a 10-inch bundt pan with 1 tablespoon softened unsalted butter, then dust the greased pan lightly with flour and tap out any excess flour.

Drain the 20-ounce can of pineapple rings into a measuring cup; reserve the juice. Pat the pineapple rings dry with paper towels to remove excess moisture.

Measure 1/2 cup pineapple juice from the reserved juice; if you have less than 1/2 cup, add water to reach 1/2 cup. Set this 1/2 cup aside for the batter.

Melt the remaining 4 tablespoons unsalted butter (microwave briefly or melt in a small saucepan). Drizzle the melted butter evenly into the bottom of the prepared bundt pan and tilt the pan to coat the surface.

Sprinkle 1 cup packed light brown sugar evenly over the melted butter in the pan.

Arrange the 8 drained pineapple rings in a single layer over the brown sugar. Place one pitted maraschino cherry in the center of each pineapple ring.

In a large bowl, combine the 15.25-ounce box yellow cake mix, the 3.4-ounce box instant vanilla pudding mix, 4 large room-temperature eggs, 1/2 cup whole milk, the measured 1/2 cup pineapple juice, 1/2 cup vegetable oil, and 1 teaspoon vanilla extract (optional). Mix on low speed or whisk just until combined—do not overmix.

Slowly pour the batter evenly over the pineapple and cherries in the bundt pan. Use a spatula to spread the batter so it covers the topping evenly.

Place the bundt pan on the center oven rack and bake 40–45 minutes, or until a toothpick inserted into the cake center comes out clean or with only a few moist crumbs.

Remove the pan from the oven and place it on a wire rack. Let the cake cool in the pan for 10 minutes.

Run a thin knife around the inner and outer edges of the pan to loosen the cake. Invert a serving plate over the pan, flip the pan and plate together, then lift the pan off the cake. Spoon any extra topping left in the pan over the cake. Serve warm or at room temperature.