3/4 cup (1 1/2 sticks) unsalted butter, room temperature, plus more for pan1 1/2 cups plus 2 tablespoons all-purpose flour (spooned and leveled) 1/2 teaspoon baking soda 1/4 teaspoon salt 1/2 cup packed light-brown sugar 1/2 cup granulated sugar 3 large eggs 1 teaspoon pure vanilla extract 2 teaspoons finely grated lemon zest 1/4 cup sour cream 3 plums, halved, pitted, and cut into eighths Confectioners' sugar, for dusting
Preheat oven to 375°F. Butter an 8-by-2-inch or a 9-inch cake pan and line bottom with a round of parchment. In a large bowl, whisk together 1 1/2 cups flour, baking soda, and salt.
Using an electric mixer, beat butter and sugars until light and fluffy. With mixer on low, beat in eggs, one at a time, until incorporated; beat in vanilla and lemon zest. Beat in 1/2 the flour mixture, then sour cream. Add remaining flour mixture; mix just until combined.
Spread batter into pan and smooth top with a knife. In a bowl, toss plums with 2 tablespoons flour and sprinkle over batter.
Bake until cake is golden, about 30 minutes; loosely tent with foil and bake until cake pulls away from side of pan and a cake tester inserted in center comes out clean, about 35 minutes more. Let cake cool completely in pan. Run knife around cake edge and remove cake from pan. Dust with confectioners' sugar before serving.