Add crumbled yeast to warm milk in a medium bowl, let stand for 3 minutes.
Whisk in the flour and sugar and mix until smooth. Cover tightly with plastic wrap and keep in warm place until it doubles in volume, about 30 minutes.
Dough
In a medium size mixing bowl add flour, sponge, milk, sugar, rum, vanilla and salt. Mix until fully incorporated.
Turn the mixture onto unfloured counter and knead for 10-15 minutes or until gluten is developed which you will confirm by window pane test.
Slowly add beaten egg to the dough, about a tbsp at the time. Each time knead the dough until the added egg is fully absorbed before adding more.
Repeat the same incremental adding process and kneading with the butter making sure the butter is fully absorbed by the dough.
Shape the soft and sticky dough into a ball, coat it with melted butter. Transfer it to a large buttered bowl, tightly cover with plastic wrap and keep in a warm place until it doubles by volume, about an hour.
Punch down the dough. Stretch and pat the dough into a buttered baking pan 17″ x 12″ x 1″. Cover with plastic wrap and let rest for 5 minutes. If the dough shrinks stretch it again to fill the pan corners.
Top the dough with rows of halved plums, skin side down. Cover with plastic wrap, keep in warm place until the dough looks raised and puffy, about 30 minutes.
Preheat the oven to 175ºC (350ºF), rack in the middle.
Streusel
In a small bowl mix together flour, sugar, butter, vanilla and cinnamon. Using your fingertips prod and squeeze ingredients until crumbly.
Sprinkle streusel evenly over the plums. Bake until the crust is golden brown, 30-35 minutes.