Mix all ingredients together using the dough hook on your mixer, at medium low for about 4 minutes. The dough should clear the side and bottom of the bowl. Add flour or water as necessary to achieve a dough that's firm but supple, tacky but not sticky.
Let the dough rest for 5 minutes, and then mix again on medium-low speed for 2-3 minutes more.
When dough sets up, wash and dry your hands and then transfer the dough to a lightly floured counter; dust the top of dough with flour to absorb the surface moisture, then knead it by hand for about 8 minutes, until smooth and elastic. The dough should be very tacky and even a little sticky, and it should feel soft and supple. It should pass the windowpane test (it doesn’t tear when a little piece is carefully stretched to translucency); if it doesn’t pass, continue kneading.
Divide the dough into four pieces. Form each piece into a ball, and rub with olive or vegetable oil. Place each piece inside its own zippered freezer bag, or on a sheet pan that has been lined with either baking parchment or a silicone baking pad. Let the pieces sit at room temperature for 15 minutes, then refrigerate the pieces that will be used the next day; freeze the pieces that will be extra (these can be pulled out and thawed in the refrigerator the day before you need them).
Pull the desired number of dough balls from the refrigerator about two hours before you plan to roll them out to take the chill off and to relax the gluten. When ready to make pizzas, flour the work surface and your hands and press out the dough with floured fingers into a flattened disk about 1 inch thick. Then flour the back of your hands and carefully lift the dough to rest on the back of your hands as a platform for gently rotating the dough, using the tips of your thumbs only on the outer edge to extend the circle of the dough. If the dough resists being stretched, lay it down on a floured surface and let it rest for a minute or two and lift it again. Each time the dough rests it will spread a little wider, but don’t pull it; just let gravity and your thumbs do all the work until it is about 9 to 11 inches in diameter.
Preheat oven to 500–550°. Transfer pizza to a lightly floured pizza peel (or onto a baking pan that has been lined with baking parchment or a silicone mat). Spoon on enough tomato sauce to just “kiss” the surface, and add the desired toppings. Slide the pizza into the preheated oven, either on the hot stone or in the baking pan, and bake up to 7 minutes till done (the crust is crisp and there’s a slight char on the crown).