Heat oven to 350 degrees F.
Melt butter in a 13 x 9-inch metal baking pan on stovetop over low heat. Remove from heat and stir in brown sugar. Drain pineapple rings, reserving 1/2 cup juice. Fit rings tightly into bottom of pan; you will need 10 to 12. Save any extra rings for snacking. Tuck a maraschino cherry in center of each ring.
In medium-size bowl, whisk flour, baking powder, salt and nutmeg. In a large bowl, beat butter and sugar 2 minutes. Add eggs; beat until blended. On low speed, beat in half the flour mixture. Pour in reserved 1/2 cup pineapple juice and the milk; beat until blended. Beat in remaining flour mixture, then vanilla.
Spread batter into pan. Bake at 350 degrees F for 40 minutes or until toothpick inserted in center comes out clean. Cool cake in pan on rack 10 minutes. If you rush to pop the cake out too soon, the pineapple rings and cherries may stick to the pan. Allow the full 10 minutes for cooling. Place a baking sheet over cake; carefully invert. If any pineapple or cherries stick to pan, gently replace on cake top.