Preheat the oven to 350F. Pour the melted butter into a 9-inch round cake pan and sprinkle the brown sugar evenly over it.
Arrange the pineapple rings over the brown sugar in a single layer and place a cherry in the center of each ring.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk the reserved pineapple juice, yogurt, oil, and vanilla until smooth.
Fold the wet ingredients into the dry just until combined, then pour the batter gently over the pineapple layer without disturbing it.
Bake for 35-40 minutes, until golden and a toothpick comes out clean. Let the cake rest in the pan for 10 minutes.
Run a spatula around the edge, place a serving plate on top, and confidently invert the cake while still warm. Cool for 15 minutes before slicing.
