Dissolve the yeast into the 3/4 cup warm milk and let is sit for 5-10 minutes until frothy.
Place the flour, sugar and salt in the bowl of a stand mixer and pour in the yeast mixture, melted warm (not hot) butter, eggs and vanilla extract. Give it an initial stir to combine the ingredients and then attach a dough hook and knead it on the bread setting ("2") for 4-5 minutes, adding the remaining 1/4 cup milk as necessary. (The dough will be sticky but should hold together fairly well. It will not be firm enough to knead into a ball, think of it more as a thick batter.) Cover it loosely with plastic wrap and set it in a warm, draft free place to rise for an hour or until about doubled in size.
Generously butter a German Backblech extended to full length or a large jelly roll pan (at least 18 inches in length and 1 inch sides but even then the crust will be thicker than with the Backblech).
Use your hands to spread the dough out across the full length of the pan, pressing it up against the sides. (It's yeast dough so it will resist, but just keep pushing it back into position the best you can. Once you put the plums on it, those will help keep it in place.) Lay the plums close together in rows over the whole length of the dough on the sheet pan. (If you want your cake a bit sweeter you can sprinkle it *lightly* with sugar or cinnamon-sugar if you prefer more cinnamon. I emphasize "lightly" because the more sugar you add the more watery the cake will be as the sugar liquifies during baking and your streusel will also "melt" in contact with it.)
Set the pan in a warm place and let it rise for up to another hour.
To make the streusel: Place all the ingredients in a medium-sized bowl and use your fingers to bring it all together. Work with the mixture until it's thoroughly combined and forms a rough sand and clumpy texture. Sprinkle the streusel over the top of the cake.
Bake the cake on the middle rack of the oven preheated to 350 degrees for 30-35 minutes or until the top is golden.
Let the cake sit for at least 10 minutes before slicing to let some of the liquid set. Slice the cake into squares and serve.
*This cake holds up well for a day or two and is even more flavorful once the juices have absorbed into the dough.