Make dough: On the morning of the day you wish to make pizza for dinner, create a sponge: In the bowl of a stand mixer, dissolve yeast in 1 cup minus 1 tbsp. cold tap water, then mix in 1 1/2 cups flour. Cover and set aside, 3 to 4 hours.
In the afternoon, mix salt into sponge, then remaining 1 cup flour. Attach dough hook and knead 25 to 30 minutes. Let dough rest, covered, 30 minutes. Divide in half and form into 2 balls. Set balls on a smooth clean surface and cover each with an inverted bowl at least 10 in. in diameter. Let rise in a warm place until puffed up and about twice their original size, 3 to 4 hours.
Make toppings: Heat oil over medium heat. Add mushrooms and salt. Cook mushrooms until their liquid has almost completely evaporated. Stir in garlic, cook 1 minute, and remove from heat.
Remove stems, ribs, seeds, and skins from peppers and cut flesh into 1/4-in. strips.
Make sauce: Mince garlic, then mash with the flat side of a chef's knife into a paste. Pulp tomatoes with a food mill or a food processor (use the shredder blade) and transfer to a bowl. Stir in salt, garlic, oil, and marjoram.
An hour before dinner, set a baking stone on middle rack of the oven. Preheat oven to 550°, or as hot as your oven will get.
About 10 minutes before you're ready to eat, dust 1 dough ball and your wooden peel liberally with flour. Using your fingertips, pat ball down into a disk, leaving rim untouched. Stretch perimeter of disk with your thumbs under the rim, then drape the dough over the backs of your hands. Turn and stretch dough into a 12-in. circle, then lay it on the floured peel. (Using a rolling pin will ruin the rim and flatten the air bubbles that give your crust its rise.) This process takes practice, so you should double the dough recipe if it's your first time.
Par-bake pizza: Prick center of untopped dough quickly with a fork and slide onto the stone in a smooth, fluid motion. Bake 2 minutes, then pull out with pizza peel.
Add toppings quickly, so the dough doesn't stick to the peel. (As you work, slide the dough back and forth every minute or so with a quick jerk of the peel to help keep it from sticking; if it does, lift dough and sprinkle more flour underneath, then jerk again.) First, sprinkle half of each kind of mozzarella onto the pizza. Then release your inner Jackson Pollock, spooning half the sauce over the pizza with a flicking motion. Add half the roasted peppers, mushrooms, and sausage. Grind on black pepper to taste.
. Slide pizza onto stone, then bake 8 to 10 minutes or until crust is puffy and golden. Take it out with the peel, grate on some parmigiano-reggiano, and scatter some torn basil leaves over the top. Drizzle with oil and dig in. Repeat with remaining dough and ingredients.
Make ahead: Dough can be formed into balls (step 2) and chilled overnight, set on a baking sheet and tightly covered with plastic wrap, or frozen for up to 2 weeks (let come to room temperature before stretching).
*Find in your local supermarket's refrigerator section next to the cheeses and butter.
Note: Nutritional analysis is per slice.