Stir yeast and warm water together in a large bowl and let stand for 15 minutes.

Add 1 tablespoon olive oil, sugar, all-purpose flour, and salt. Use a wooden spoon to stir until a very soft, sticky dough forms. While stirring, incorporate any dough that sticks to the sides of the bowl.

Drizzle over a tablespoon of olive oil, and rub some on your hands. Pick up dough, and with your fingers under the dough pushing gently up, stretch the sides down and under several times while rotating the dough, in order to form a relatively smooth ball with some surface tension on top. Place dough ball into the bowl, smooth side up, cover the bowl, and refrigerate overnight.

The next morning, pull out dough and let rise at room temperature until doubled in size, about 1 1/2 hours.

Generously oil a work surface with about 1 tablespoon olive oil, and transfer dough to the work surface. Press into a large rectangle, and then fold into thirds one way, and then the other, forming a small rectangle, about 6x9 inches.

Generously oil a sheet pan with about 2 tablespoons olive oil, and transfer dough rectangle to the sheet pan. Press dough out to about 1/2-inch thick. Cover; let proof at room temperature until dough has spread out, risen slightly, and surface has bubbles, 1 1/2 to 2 hours.

Meanwhile, wrap plum sections with prosciutto and refrigerate until needed.

Preheat the oven to 475 degrees F (245 degrees C).

Sprinkle dough with rosemary. Push wrapped plum sections deep into the dough in a 3x4 pattern. Drizzle top lightly with olive oil; sprinkle with sea salt.