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1
Preheat the oven to 350 degrees F, with a rack in the lower third. Butter a 9-by-2-inch round cake pan. Line the bottom with parchment paper and butter the parchment. Dust the pan with flour, tapping out the excess.
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2
Stir together the flour, baking powder, salt, and baking soda in a small bowl. Set aside. Stack the lemon verbena leaves (if using), roll up tightly lengthwise, and cut them crosswise into fine ribbons. You will want 2 to 3 packed teaspoons.
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3
In the bowl of a standing mixer fitted with the paddle attachment (or with a handheld mixer), beat together the butter and granulated sugar on medium speed until light, about 5 minutes. Mix in the eggs, one at a time, beating well and scraping down the bowl after each addition. Mix in the sour cream, vanilla, and reserved lemon verbena (or lemon zest) until well combined. On low speed, add the flour mixture just until combined. (The batter will be thick.)
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4
Spread half of the batter evenly into the bottom of the prepared pan. Sprinkle with 1 tablespoon brown sugar and top with 12 of the plum halves, cut side down. Dollop and spread the remaining batter over the plums. Arrange the remaining 12 plum halves, cut side up, over the top. Sprinkle the remaining 1 tablespoon brown sugar over the plums.
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5
Bake until the cake is golden and pulling away from the sides of the pan and a toothpick inserted near the center tests clean (assuming you haven't hit a plum), 50 to 55 minutes, rotating the pan front to back a little past halfway through baking. Let cool in the pan on a wire rack for 20 minutes.
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6
Run a thin knife around the inside edge of the pan to loosen the cake sides. Invert a flat plate over the pan. Using oven mitts if needed, grasp the plate and pan tightly together on both sides and invert the plate and pan to release the cake onto the plate. Lift off the pan and peel off the parchment. Invert the cake again onto a serving plate.
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7
Serve warm or at room temperature, with whipped cream, if desired.
