Preheat oven to 375 degrees F (190 degrees C). Grease a 9-inch cake pan, and line the bottom with a round piece of parchment paper.
In a large bowl, whisk together 1 1/2 cups flour, baking soda, salt, and cinnamon. In a separate bowl, beat butter, brown sugar, and white sugar with an electric mixer until light and fluffy; beat in eggs one at a time, then beat in vanilla extract and lemon zest. Mix the butter mixture into the flour mixture, alternating with yogurt until the mixture forms a smooth, even batter. Spread the batter into the prepared cake pan. Place the plum slices into a bowl, and toss with 2 tablespoons of flour. Arrange the plum slices onto the cake in a decorative pattern.
Bake in the preheated oven until browned, about 30 minutes. Loosely cover the cake with foil, and bake until a toothpick inserted into the center of the cake comes out clean and the cake pulls away from the sides of the pan, 30 to 40 more minutes.
Let cake cool completely in pan. Run a knife around the edge of the cake to loosen, and remove from pan. Dust with powdered sugar before slicing.