Prepare glaze: beat butter, sugar, honey, brown sugar, vanilla, and salt until smooth and well-blended.
Cut plums in half and remove pits. Steep them in a little sugar and the rum.
Spread a thick layer of glaze over the bottom of a 9" silicone cake pan. You may have more glaze than you need. You can judge how much you want to use.
Take the plums and arrange them in concentric circles in the pan until the bottom of the pan is covered with plums.
Prepare cake batter: mix the dry ingredients and set aside. Mix butter and sugar on low speed to blend and then mix on medium speed for 3 minutes until light and creamy. Mix in vanilla. Add the eggs one at a time and mix to incorporate. Mix in the milk. Add the flour mixture in three batches and mix until just blended.
Pour the batter into the pan and spread carefully over the plums. Bake for 15 minutes and then rotate pan and back for another 20 to 25 minutes or until cake tester comes out clean.
Cool cake on a rack for 30 minutes or so. Then run a knife around the edge of the pan and invert on to serviing dish. Serve warm. I like to serve with creme fraiche whipped cream or vanilla ice cream.