In a large bowl, combine yeast and 2 1/2 cups flour with 2 cups water; whisk to combine. Let stand 15 minutes.
Add remaining 2 1/2 cups flour and salt; mix until well combined. Turn dough out onto a lightly floured work surface; knead until wet and tacky, but not sticky, 8 to 10 minutes. Transfer to a well-oiled bowl and cover with plastic wrap. Let stand until doubled in size, 3 1/2 to 4 hours.
Oil a large rimmed baking sheet and press dough evenly into baking sheet. Let rise until puffy, about 1 hour.
Preheat oven to 500 degrees. Cover dough with Pecorino Pepato and lemon slices and sprinkle with rosemary leaves and salt; drizzle with extra-virgin olive oil. Transfer to oven and bake for 15 minutes. Rotate baking sheet, and continue baking until lemons and crust are golden brown, about 15 minutes more.
Remove bread from baking sheet and transfer to a wire rack to cool at least 10 minutes before serving.