Sprinkle the yeast over the water in a 2-cup measuring cup and let stand until the yeast dissolves, about 5 minutes.
Fit a heavy-duty mixer with the dough hook. Combine the flour, brown sugar, and salt in the mixer bowl and stir to blend. If using the orange zest, stir it into the yeast mixture. With the mixer running, gradually pour in the yeast mixture. Continue mixing, stopping the machine once or twice to scrape down the sides of the bowl, until the flour and liquid are blended. Increase the speed to high and knead with the hook until a very smooth and sticky dough forms, about 7 minutes. (Yes, 7 minutes!)
Drizzle a 9-by-13-inch baking dish generously with enough oil to coat the bottom of the dish. Using a silicone spatula, transfer the dough to the prepared dish (the dough will be wet). Fold the dough into thirds, like a business letter. Cover with plastic wrap and refrigerate overnight or for up to 2 days, repeating the folding once or twice a day.
Brush four 2-cup-capacity food jars or storage containers with oil. Using a bench knife, large cleaver, or chef’s knife, cut the cold dough into 4 even pieces (about 9 oz. each). On a lightly oiled surface, shape each piece into a round. Transfer one dough piece to each jar and seal. Refrigerate the dough overnight or for up to 4 days.
Position racks in the upper and lower thirds of the oven and preheat to 500°F.
Fill a shallow bowl with flour. Dust two heavy large sheet pans lightly with flour. Working with one dough piece at a time, dip the dough round into the bowl of flour to lightly coat. Holding the dough at the top edges with both hands (like a steering wheel), carefully stretch the dough into a 9-to-10-inch round by rotating it and keeping your hands in the same position. Transfer the round to the prepared pan. Repeat with another piece of dough and pan. Brush the pizzas lightly with oil. Scatter 2 tbsp. of the ice over the center of each pizza. Bake until the pizzas are golden brown, 10–12 minutes, alternating the baking position about halfway through baking. Immediately sprinkle 1⁄4 cup cheese over each pizza. Season the pizzas very generously with pepper and drizzle with oil. Toss the arugula with enough olive oil to coat and the remaining 1⁄4 cup cheese. Top the pizzas with half the arugula and serve. Repeat with the remaining pizzas and arugula.