1) Mix all of the ingredients to make a soft, supple dough. Knead for 5 minutes, divide the dough in half, cover with lightly greased plastic wrap, and let rest and relax for 15 minutes (or for up to an hour or so; work it into your schedule as you see fit).
2) Grease two 12" squares of parchment paper. Use your greased fingers to press each piece of dough on the parchment into an 11" to 12" circle about 1/8" thick. Brush or spray the crusts with olive oil, and let them rest for about 30 minutes, while you preheat your oven to 450°F (with a pizza stone inside, if you have one).
3) Place the crusts with their parchment directly on the stone, or onto a baking sheet. Bake until they're just starting to brown around the edges, about 4 minutes. Remove them from the oven, top with your favorite toppings — we've used pesto, sliced tomatoes, and mozzarella here — and bake for an additional 6 minutes, until everything's warm and bubbly.
4) To make grilled pizza: Be prepared to grill your pizza within 15 minutes of shaping it; you don't want it to rise too much. So, make sure your barbecue grill is heated (or cooled) to medium-hot by the time the dough is ready to grill.
5) Set the rack 3" to 4" above the fire. Take one circle of dough, on its parchment, and swiftly but carefully turn it (dough down, parchment on top) onto the grill. Peel off the parchment.
6) After 1 minute, turn the crust over; it should be stiff enough to turn quite easily (if not, your grill isn't hot enough). Layer with toppings. This is not the time to pile on the meat, cheese, veggies, etc. Since the pizza will be cooking very briefly, it's better to top with just a minimal amount of stuff: thinly sliced veggies, a thin layer of cheese, etc.
7) Bake an additional 5 minutes or so, with the cover on (if your grill has a cover), or until the filling is hot and the cheese is melting. Adjust the temperature of the grill if the bottom is browning too quickly. And, move the pizza around on the grill if one side or the other starts to get too brown on the bottom. Repeat the grilling process with the other pizza.
Yield: two 12" thin-crust pizzas.