Make sure all ingredients are at room temperature before starting.
Preheat the oven to 350°F (180°C) and generously butter a 9 inches (25 cm) springform baking tin.
Sprinkle ¼ cup (50 grams) sugar into the base of the tin. Arrange the plums in an even layer over the sugar and set aside.
Add the flour, baking powder, cinnamon, and salt to a medium bowl and whisk to combine. Set aside.
In a large mixing bowl, beat 1 cup (200 grams) sugar and the butter for 3-4 minutes, until light and fluffy.
Add the eggs one at a time, beating between each addition. Mix in the vanilla.
Add half the flour mixture to the butter mixture and beat on low speed until just mixed.
Mix in half the milk on low speed. Add the remaining flour mixture and beat again, then add the remaining milk and mix until just combined.
Spread the cake batter in an even layer over the plums, using a spatula to even it out.
Bake for 35-40 minutes, or until evenly golden and the cake is pulling away from the edges of the tin. Insert a skewer into the centre of the cake. If it comes out clean, with no crumbs, the cake is finished.
Cool for 10 minutes in the tin before carefully removing the sides and cooling fully on a wire rack.
Place a plate on the cake and carefully flip over, then remove the base of the tin from what's now the top of the cake. Slice and serve.
Leftover cake will keep for a couple of days in an airtight container.
Notes
Be sure to beat on low speed when adding the flour and milk in increments. This is for two reasons: first, mixing on high will cause the batter to make a mess, and two, over-mixing will make for a less pleasant, gummy texture. You want to mix until just combined and no further.
If your pan is a bit older and you’re worried about batter sticking to it, simply line the base with a round of parchment paper after buttering. Sprinkle the sugar over the paper.
You can bake the cake in a slightly smaller tin (20cm / 8 in. instead of 25cm / 9 in.) but increase the baking time by about 5 minutes. Make sure to do a toothpick test if changing the tin size.