Add the egg and egg yolk to a large mixing bowl and beat well. Sift the powdered sugar into the bowl, then add all the remaining ingredients except the plums and demerara sugar.
Mix using a stand mixer fitted with a paddle attachment or your fingers until the mixture resembles a crumbly dough. Remove 1/3 of the dough (for the streusel topping) and transfer it to a bowl. Refrigerate.
Mix the remaining dough a little longer, just until it comes together (don’t overmix!).
Grease a 9x13-inch (23x33 cm) baking pan with butter and line it with parchment paper.
Press the remaining dough evenly into the bottom of the pan, forming a 1-inch rim. Refrigerate for about 20 minutes.
Meanwhile, wash and halve the plums, removing the pits. If using larger, regular plums, cut them into quarters. If using smaller Italian/prune plums, just halve them. Make sure to use the correct amount of plums depending on the variety — regular plums release more liquid than Italian/prune plums, so you’ll need to use fewer of them.
Preheat the oven to 350°F (180°C).
Once the dough is chilled, arrange the plums, cut side up, tightly over the dough. They should overlap. It may seem like too many plums, but it isn’t — the streusel will absorb the extra juices and if you use less, the cake will be dry.
Crumble the reserved 1/3 dough over the plums to form the streusel topping.
Sprinkle demerara sugar over the top.
Bake for 40–45 minutes, or until the streusel is golden and the plums are bubbling.
Transfer to a wire rack to cool.
Tastes great slightly warm or at room temperature.
Enjoy!