Thin Crust Pizza

Ingredients

• 3 cups (16 1/2 ounces) bread flour, plus more for work surface (see note)
• 2 teaspoons sugar
• 1/2 teaspoon instant or rapid-rise yeast
• 1 1/3 cups ice water (about 10 1/2 ounces) (see note)
• 1 tablespoon vegetable oil, plus more for work surface
• 1 1/2 teaspoons table salt
• 1 (28-ounce) can whole peeled tomatoes, drained and liquid discarded
• 1 tablespoon extra-virgin olive oil
• 1 teaspoon red wine vinegar
• 2 medium garlic cloves, minced or pressed through garlic press (about 2 teaspoons)
• 1 small shallot, minced (optional)
• 1/4 teaspoon crushed red pepper (optional)
• 1 teaspoon table salt
• 1 teaspoon dried oregano
• 1/4 teaspoon ground black pepper
• 1 ounce finely grated Parmesan cheese (about 1/2 cup)
• 8 ounces whole milk mozzarella, shredded (about 2 cups)