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Four hours before cooking, heat a wood-burning pizza oven. Alternately, heat a pizza stone in a 500 degree F oven for 1 hour.
For the pizza dough: In a stand mixer fitted with the dough hook, combine the yeast, lukewarm water, and 1/2 cup of the bread flour. Mix well and let sit for 30 minutes, or until bubbly like foamy beer.
In a separate medium bowl, whisk together the remaining 3 1/2 cups bread flour and the salt until evenly combined.
Add 3/4 cup cold water and the olive oil to the yeast mixture. Turn on the mixer and begin adding the flour mixture in increments, then mix for 5 minutes, until the dough starts creeping up the dough hook and detaching from the sides of the bowl.
Grease a large bowl with oil and transfer the dough to the bowl. Turn the dough to coat its surface with oil. Cover the bowl loosely with a tea towel. Let the dough rise until doubled in size, about 2 hours. Punch the dough down, then let rise another 1 hour.
For the topping: Spread 1/4 cup of pear jam on top of the dough, leaving a 1-inch border. Using a vegetable peeler, shave some Pecorino Romano on top; season with salt and pepper and drizzle with olive oil. Place the pizza on the oven floor and cook until the cheese is just melted and the dough is golden-brown and crisp, about 3 minutes. (If using a home oven with a pizza stone, increase the baking time by 2 minutes.)
Scatter 1/2 of a sliced pear on top of the cheese, drizzle with some more olive oil and serve hot. Repeat with 3 remaining dough balls.