Preheat the oven to 350°F.
For the schmear: In the bowl of a stand mixer fitted with the paddle or a food processor, combine the butter, honey, rum, brown sugar, and vanilla; beat until smooth and well blended. Spread 1 cup of the schmear over the bottom of a 9-inch silicone baking pan. Sprinkle lightly with salt. Set aside.
To cut the citrus: trim off each end. Stand the citrus upright a cut, flat end and cut away the peel and pith with a sharp knife, following the contours of each citrus. The slice the citrus into rounds, about ¼ inch thick.
For the cake batter: place the butter and sugar in the bowl of a stand mixer fitted with the paddle or food processor and beat for a few minutes until light and creamy, stopping to scrape down the sides as necessary. Add the vanilla and eggs, one at a time, beating until the first one is incorporated before adding the second and scraping down the sides as necessary. Beat in the milk. Add the flour and baking powder; beat until just combined.
Pour the batter into the pan and spread over the citrus. Bake for 15 minutes. Rotate the pan for even browning and bake for another 20 to 25 minutes, until a cake tester or wooden skewer inserted in the center of the cake comes out clean. Cool the cake in the pan on a cooling
Run a knife around the edges of the cake, invert onto a serving platter, and serve warm, with Greek yogurt and a drizzle of honey or date syrup.