Stir the yeast and lukewarm water together in a large bowl or mixer bowl.  Add 1/4 cup all-purpose flour and semolina.  Mix well.  Let sit until bubbly, about 30 minutes.

Combine remaining flour and salt in a separate bowl.  Add to the yeast mixture along with the cold water and olive oil.  Mix well to form the dough.

Turn dough out onto a lightly floured board and knead with hands for about 10 minutes until dough is smooth and elastic.  Or use a mixer with a dough hook and knead about 5 minutes.

Place dough in a lightly oiled bowl and turn to coat all sides with oil.  Cover bowl loosely with plastic wrap.  Let rise in a warm place until doubled in size, 1 to 2 hours.  Punch dough down, and let rise another 45 minutes.

Divide dough into 2 equal disks (or 4 if you would like small pizzas).  Let rest 30 minutes before shaping.  Lightly flour a work surface.  Using your fingers or heels of your hands, stretch the disks out to 10" shapes.

Preheat the oven to 375°F.  Line a large baking sheet with parchment paper and set aside.

Toss potatoes with 1 tablespoon olive oil and 1 teaspoon salt in a large bowl.  Arrange potatoes in a single layer on the prepared baking sheet.  Bake until edges begin to turn golden brown, 15 to 20 minutes.  Remove from oven and let cool.

Place the pizza stone (if using) on a shelf positioned in the lower third of the oven.  Increase the oven temperature to 475°F.

Bring a large pot of salted water to boil.  Add broccoli rabe and blanch for 30 seconds; drain.  Plunge broccoli rabe into a bowl of ice water.  Cool and drain again.  Lay in one layer on a kitchen towel to thoroughly dry.  Cut into 1 1/2" to 2" pieces.

Heat one tablespoon olive oil in a skillet over medium heat.  Add minced garlic and red pepper flakes.  Sauté briefly, 30 seconds.  Add broccoli rabe and 1/2 teaspoon salt.  Sauté one minute.  Remove from heat.  Taste and add more salt if necessary.

To facilitate the transfer to the preheated pizza stone (if using), line work area with a large sheet of parchment paper.  Or place prepared dough directly on baking sheet.   Lightly brush pizza crusts with olive oil.  Rub all over with smashed garlic cloves.

Arrange one layer mozzarella cheese over crusts.  Top with one layer of potatoes and broccoli rabe.  Sprinkle one tablespoon chopped rosemary over each crust.  Top with grated Pecorino cheese.

Before serving, sprinkle with freshly ground black pepper.  Garnish with fresh rosemary leaves, if desired, and drizzle with extra-virgin olive oil.