Prepare the Oven and Pan: Preheat the oven to 350°F (175°C). Lightly grease a 9-inch springform cake pan with baking spray to help prevent the cake from sticking.
Combine the Dry Ingredients: In a medium mixing bowl, whisk together the all-purpose flour, baking powder, ground cinnamon, and salt until evenly distributed. Set the mixture aside.
Cream the Butter and Sugar: Place the softened butter and granulated sugar in a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed for approximately 3 minutes, until the mixture becomes pale, light, and fluffy. Incorporate the Eggs and Vanilla: Add the eggs and vanilla extract to the creamed butter mixture. Beat until thoroughly combined, then scrape down the sides and bottom of the bowl to ensure the ingredients are evenly incorporated.
Alternate the Flour Mixture and Milk: Reduce the mixer speed to low. Add the dry ingredients in three portions, alternating with additions of the room-temperature milk between the flour additions. Mix just until the ingredients come together, scraping down the bowl as needed. Give the batter one final mix to ensure it is evenly combined. Fill the Prepared Pan: Transfer the batter into the greased springform pan. Use a spatula to spread it evenly across the pan, smoothing the surface so the plums can be arranged on top.
Arrange the Plums: Distribute the pitted, quartered plums over the batter with their skin sides facing upward. Cover the surface with the fruit as evenly as possible. Sprinkle additional granulated sugar over the plums if desired.
Bake the Cake: Place the pan in the preheated oven and bake for approximately 55 minutes. The cake is ready when the top is golden brown and a toothpick inserted into the center comes out clean. If the toothpick still shows wet batter, continue baking for a couple of additional minutes and check again. Cool in the Pan: Remove the cake from the oven and let it rest in the pan for 10 minutes. This initial cooling period helps the cake settle before you remove it from the pan.
Release the Springform Ring: Carefully run a knife around the inside edge of the pan to loosen any cake that may be sticking. Release the springform mechanism and lift away the outer ring.
Cool Completely Before Serving: Allow the cake to cool completely to room temperature before transferring it to a serving plate or cutting it into slices. This helps the cake set properly while preserving its moist interior and delicate crumb.
