Special equipment: a pizza stone or baking sheet
For the dough: Stir together the warm water, honey and yeast in a measuring cup or small bowl. Let sit until a small layer of foam develops at the top, 3 to 5 minutes. (If this doesn't happen, your yeast is old; discard it and try again with new yeast.)
Combine the flour and 1/2 teaspoon salt in a medium bowl and make a well in the center. Add the yeast mixture and oil to the well and incorporate with a wooden spoon until a sticky dough forms. Scrape down the sides of the bowl with a silicone spatula to reincorporate any dough stuck to the sides. Cover the bowl tightly with plastic wrap or a damp kitchen towel and keep in a warm place until the dough has doubled in size, about 1 1/2 hours.
Knead the dough on a floured surface just until smooth, a few seconds. Divide the dough into 2 balls, cover with plastic wrap or a damp kitchen towel and let rest on the counter for 30 minutes.
For the sauce: Put the tomatoes in a small bowl and rinse the can with about 2/3 cup of water into the bowl.
Add the oil, garlic, 1/4 teaspoon salt and crushed red pepper to a large skillet. Cook over medium heat, stirring, until the garlic just starts to turn golden, 3 to 4 minutes. Add the tomato mixture and simmer, stirring occasionally, until the sauce thickens, 15 to 20 minutes.
For the pesto: Preheat the oven to 400 degrees F. Spread the pistachios on a baking sheet and toast, tossing once, until slightly browned and aromatic, about 8 minutes. Let cool, then pulse in a food processor until the texture of coarse sand. Add the arugula, parsley and 1/4 teaspoon salt and pulse until the mixture is evenly chopped. Drizzle the oil through the feed tube with the machine running until well incorporated.
When you are ready to bake the pizza, place a pizza stone in the bottom of the oven and heat it to 450 degrees F. If you do not have a pizza stone, preheat a baking sheet that has been flipped over bottom-side up. Cut two 12-inch squares of parchment and dust with flour.
On a floured surface, stretch one ball of dough to a 12-inch round, leaving a thick 3/4-inch border on the edge. Slide the dough onto one of the parchment squares, then slide the square onto the back of a baking sheet. Brush the entire round with 1/2 tablespoon oil. Spread the dough up to the border with half the tomato sauce. Dollop the pizza with half the pesto using a teaspoon. Sprinkle with 1/3 cup of the mozzarella and a pinch crushed red pepper. (Don't worry if it looks like too little cheese. It will melt and spread.) Slide the pizza and parchment from the baking sheet onto the hot pizza stone.
Bake the pizza until the edges turn golden brown, 6 to 8 minutes, rotating halfway through cooking. Let cool for 2 minutes before slicing. Repeat with the remaining dough and toppings.
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