You may substitute regular plums in this recipe, but the smaller Italian prune plums are sweeter. This is a great cake to make for breakfast, because the dough rises overnight in the refrigerator.
In a small bowl, whisk together warm water and yeast; set aside. Put sugar, 2 cups flour, ¾ teaspoon salt, egg, and 1 stick butter in the bowl of a mixer or food processor fitted with a dough blade. Add yeast mixture and pulse until a ball forms. It should be sticky; add more water, a tablespoon at a time, if needed. Remove dough from processor and transfer to a lightly oiled bowl. Cover with plastic wrap and refrigerate overnight. It will rise only slightly.
When dough is ready, adjust oven rack to middle position and preheat to 400°F. Remove dough from refrigerator and set aside. Halve plums (if using regular plums, cut into quarters) and remove stones; set aside.
Prepare crumb topping: In a small bowl, combine ⅓ cup flour, ½ teaspoon salt, 2 tablespoons butter, and brown sugar. Rub mixture with your fingers until crumbly; then stir in almonds and set aside.
Grease a 9-inch springform pan. Remove dough from bowl and, on a lightly floured work surface, press with your fingers into a 9-inch circle. Place dough in pan. Leaving a ½-inch border around edge of dough, arrange plums snugly, like fallen dominoes, in circles over surface of dough.
Sprinkle crumb topping on plums; then bake until topping and crust are light brown and plum juices run, 40–45 minutes.