In the bowl of a stand mixer fitted with the paddle attachment, combine lukewarm water with the yeast and the sugar. Let sit until foamy, about 5 minutes.

Add olive oil, then add flour and salt. Mix on medium-high speed for about 5 minutes, or until the dough is elastic and ropey.

Grease a 13-by-18-inch sheet pan with a little oil, then line with parchment. Drizzle 4 more tablespoons oil in the pan. Scrape dough onto the pan but don’t spread it out. Leave it where it flops. Top the pan with another, overturned sheet pan to cover the dough without touching it. Let dough proof in a warm place until it spreads out in the pan and puffs slightly, about 1 hour.

Transfer the overturned sheet pan that was covering the dough to the oven (still overturned) to heat. Turn oven to 450 degrees.

Oil your fingers, then gently pat and press the dough into an even layer to cover most of the bottom of the sheet pan, oiling your fingers as you go. Take your time with this: The dough is sticky. Let rise uncovered until dough fills the pan and puffs slightly, 35 to 45 minutes.

Meanwhile, prepare the tomatoes: Drain and coarsely chop them. Add them to a bowl and stir in the oil and salt.

Spread about ½ cup tomato mixture over dough in a thin layer. Sprinkle red onion or garlic over the pizza, if using. Drizzle lightly with oil and sprinkle with oregano, red-pepper flakes and flaky salt, if you like.

Place the pan onto the heated sheet pan in the oven. Bake pizza until lightly golden brown on top, 22 to 30 minutes.

Remove the pizza from the oven and sprinkle with mozzarella, if using. Return to the oven until the cheese has just melted, about 5 minutes. Top with torn basil leaves or arugula, and drizzle with olive oil before serving.