Preheat the oven to 350°F and butter the inside of a 9-inch springform pan.
Cream together the butter and 1 cup of sugar in a medium bowl until light and fluffy. You can use an electric mixer, but I find a wooden spoon and a little elbow grease to the job just fine.
Add in the eggs, one at a time, making sure each is fully incorporated.
Mix in the flour, baking powder and salt until just combined.
Spread the batter into the pan and smooth the top.
Arrange the halved plums cut-side-down, then use your fingers to gently press them into the batter.
Squeeze the lemon juice over the fruit, then mix together the remaining tablespoon of sugar and cinnamon, and sprinkle over the top.
Bake for about 45 minutes to an hour, or until the cake is golden brown and a toothpick inserted into the center comes out clean.
Allow the cake to cool on a rack for at least 30 minutes prior to cutting. Serve warm or at room temperature. The cake is also excellent served cold after chilling in the fridge overnight.