Preheat the oven to 356°F / 180°C. Wash the plums and remove the pits. Leave the skins on — they add flavor and color. No need to slice them perfectly; rustic chunks bake up juicier and tastier.
Prepare an 8-inch (20 cm) round cake pan. Line the base with parchment paper and grease the pan well with butter, making sure to coat the sides for even browning.
In a bowl (or food processor), whisk together the softened butter, buckwheat flour, eggs, sugar (if using), milk, and a pinch of salt until smooth. If the butter is cold, melt it gently before mixing so it blends in properly.
Place the plums into the pan and sprinkle with cinnamon. For extra flavor, drizzle over a little rum and toss lightly so the fruit is evenly coated.
Pour the buckwheat batter over the plums. Bake for 45–50 minutes. If the top browns too quickly, cover loosely with parchment paper or foil.
The clafoutis is ready when the top is golden and the plum juices bubble at the edges. Run a knife around the sides to loosen, let it cool slightly, then slice and serve. Dust with powdered sugar or scatter sliced almonds on top, if you like.