1Make the cake dough: In a small bowl, mix milk with 2 tablespoons hot water (this will make the lot lukewarm - easier, I think, than bringing your milk to room temperature); stir in the yeast and let it sit until it foams a bit.
2Beat together the butter, sugar and salt, then beat in the egg. Add flour and milk mixture alternately, beginning and ending with the flour mixture. Stir until you have a sticky dough, then turn it out onto the countertop (resist the urge to add more flour) and knead for a few minutes, until soft and smooth.
3Pat, press, stretch and nudge the dough into a buttered baking dish that is around 9"x13" and at least 2 inches deep. Cover with plastic wrap or a tea towel, and let it rise while you go to the beach - 2-3 hours.
4Preheat oven to 350F. Lay the slices of plum in rows over the surface of the dough, which really won't have risen that much. In a small bowl, stir the honey, 2 tablespoons water and the vanilla together with a fork. In a larger bowl beat the butter, sugar and salt until smooth and light, then beat in the egg. Add half the flour, then the honey mixture, then the rest of the flour, scraping down sides of bowl between each addition and stirring just until blended.
5Spoon the topping in large dollops over the plums and gently spread overtop with a spatula. Bake for about an hour, until golden; it will still be slightly soft (gooey) in the middle. Cool completely before serving - really, do - plums hold onto their heat and you won't be able to taste it properly until it's cooled.