Step 1

Heat the oven to 375°F with a rack in the middle position. Mist an 8½-by-4½-inch loaf pan with cooking spray, then line it with an 8-by-14-inch piece of kitchen parchment, allowing the excess to hang over the long sides of the pan.

Step 2

To make the caramel-plum layer, in a small saucepan, combine the butter and sugar. Cook over medium, stirring occasionally, until thick and well combined, about 2 minutes; the sugar may remain slightly granular. Transfer to the prepared loaf pan and, using a silicone spatula, distribute in an even layer. Place the plum slices in the caramel, overlapping them as needed to fit. Sprinkle the salt over the fruit; set aside.

Step 3

To make the cake, in a medium bowl, whisk together both flours, the cardamom, baking powder, baking soda and salt. In a small bowl or liquid measuring cup, whisk together the eggs and vanilla.

Step 4

In a stand mixer with the paddle attachment, beat the sugar and orange zest on medium until fragrant, about 1 minute. Add the butter and beat on medium-high until light and fluffy, scraping the bowl as needed, about 3 minutes. With the mixer running on low, gradually add the egg mixture, then beat on medium until well combined, about 1 minute. Scrape down the bowl. With the mixer running on low, add the dry ingredients and mix, scraping the bowl once or twice, just until the mixture is evenly moistened, about 1 minute. Fold the batter by hand with the spatula, scraping the bottom and sides of the bowl to ensure no pockets of flour remain. The batter will be thick.

Step 5

Scrape the batter onto the fruit in the loaf pan, then spread in an even layer and smooth the surface. Bake until the top is deeply browned and a toothpick inserted at the center comes out clean, 55 to 60 minutes.

Step 6

Cool in the pan on a wire rack for about 15 minutes; the center of the cake may sink slightly during cooling. Slide a paring knife between the short ends of the cake and the pan to loosen, then invert the cake onto a platter. Lift off the pan and peel off the parchment. Cool to room temperature.