Heat the milk in a small saucepan until hot but not boiling. Pour the milk into a large heat-safe mixing bowl. Add the sugar and butter, then whisk to combine.
Check the temperature of the milk mixture with a finger. It should feel just warm, but not hot. Sprinkle the yeast over the milk mixture and set aside for 15 minutes. After this time, the yeast should bloom and expand.
Whisk the egg into the mixture.
Add the flour and salt, mixing with a wooden spoon or spatula until a shaggy dough forms. Turn the dough out onto a lightly floured work surface and knead until soft and smooth, 8-10 minutes.
Place the kneaded dough back into the bowl and cover with a tea towel or plate. Set the bowl in a warm, draft-free spot for about an hour, or until the dough has doubled in size.
Once the dough has risen, gently punch it down. Turn it out onto a lightly floured surface and roll it into a large rectangle to fit your largest baking sheet or one that is roughly 12x16 inches (40x30cm).
Preheat the oven to 350°F (180°C) and line a large baking sheet with parchment paper.
Place the plums in a thick, overlapping layer over the dough, making sure to go right to the edges.
Once the oven is hot, bake the cake on the centre rack for 30-35 minutes. It can be hard to tell when it's done due to the juice from the plums, but it should look golden and the edges should feel firm but not hard when pressed with a fingertip.
Remove the cake from the oven and cool fully on a wire rack. Cut into 16 squares and serve plain or with whipped cream.
Notes
Check that your yeast isn't expired before beginning.
Rising dough in the oven with the light on is great, or near a warm radiator.
No second rise is needed once the dough is rolled out.
Using this many plums on the cake makes for a lot of juice during baking, and will make the edges of the cake pink and soft. This is normal and delicious.