Crank up the oven to 350°F (176°C). Generously butter a 9-inch springform pan, line it with parchment paper, and butter the parchment.
Whisk the 1 cup all-purpose flour, 1 teaspoon baking powder, and large pinch salt in a large bowl.
Beat the 1 stick (4 oz) unsalted butter and 3/4 to 1 cup granulated sugar (depending on the tartness of the plums) in the bowl of a stand mixer, or in a large bowl with a handheld mixer, until light in color, 3 to 5 minutes.
Add the flour mixture to the bowl and then the 2 large eggs, 1 at a time, mixing just until combined.
Spoon the batter into the pan and smooth the top with an offset spatula. Dot the top of the batter with the 12 Italian purple plum halves or red plum quarters, skin side up.
Mix the 2 tablespoons granulated sugar, 1 teaspoon
ground cinnamon, and 1/2 teaspoon ground ginger in a small bowl.
Sprinkle the fruit with the cinnamon sugar and squeeze the 1/2 lemon over the top of the batter, adjusting the amount to the tartness of the fruit.
Bake the plum torte until the cake is golden and the plums are bubbly, 50 to 60 minutes. Cool on a rack, then unmold.