For the dough: In a mixer with a dough hook attachment, blend 4 cups (1 quart) ice cold water, the salt, yeast, pepper and sugar and mix well; let rest for 10 minutes. Next, add the flour and oil and mix until smooth, 3 to 4 minutes. Oil a baking sheet. Portion the dough into two rounds and place on the baking sheet. Allow to rest and rise until doubling in size, about 1 hour.
Working with one ball of dough at a time, spread the dough evenly, forming a crust about 13 inches in diameter. Transfer to a round pan and allow to rise for 30 minutes; repeat with the other dough ball.
Preheat the oven to 300 degrees F.
For the pizzas: After rising, "dock" each crust with your fingertip to form small pockets in the dough, 20 to 30 pockets on each. Pour about 2 ounces of sauce over each crust to cover the dough and fill the pockets. Bake for 20 minutes to form the crust and allow the sauce to dry into the dough.
Raise the oven temperature to 450 degrees F.
Evenly spread the remaining sauce to cover the cooked crusts, leaving a 1/2-inch border unsauced. Next, spread 2 ounces of cheese over the sauce on each pizza, followed by the toppings. Finish with a sprinkling of more cheese. Bake until the cheese is melted, 12 to 15 minutes.