Make the dough:
Divide pizza dough balls evenly into 4 pieces total (about 8 ounces each). Shape each dough piece into a taut ball, and place, seam side down, on a well-floured surface. Cover loosely with plastic wrap, and let rest until dough is room temperature, 1 hour to 1 hour and 30 minutes. Meanwhile, place a baking stone or steel on middle oven rack, and preheat oven to 450°F for 30 minutes.
Make the garlic ranch:
Process tofu, vegan mayonnaise, dill, garlic, garlic powder, rice vinegar, red wine vinegar, salt, and onion powder in a blender until smooth, about 30 seconds. Set aside.
Make the wild mushrooms:
Heat a large skillet over medium-high. Add butter; cook, stirring constantly, until melted, about 5 seconds. Add shallot and garlic; cook, stirring constantly, until fragrant, about 15 seconds. Add mushrooms, thyme, salt, and pepper; cook, stirring often, until mushrooms are tender, 3 to 4 minutes. Remove from heat; transfer mixture to a medium bowl.
Place 1 dough ball on a well-floured work surface. Using your fingers, stretch dough into a 10-inch round. Transfer dough round to a lightly floured pizza peel.
Spread 3 tablespoons garlic ranch over dough round, leaving a 1/2-inch border. Top with 11/2 ounces (heaping 1/4 cup) wild mushrooms, 11/2 ounces (about 1/2 cup) mozzarella shreds, and 3/4 ounce (about 1/3 cup) shaved brussels sprouts.
Carefully slide pizza onto preheated baking stone in preheated oven. Bake until pizza is bubbly in the center, brussels sprouts are starting to crisp, and crust is charred in spots, 15 to 18 minutes. If needed to get a nice char on top, increase oven temperature to broil with oven rack 8 inches from heat; broil pizza 2 to 3 minutes. Transfer pizza to a cutting board, and drizzle lightly with white truffle oil. Repeat process with remaining dough balls, garlic ranch, wild mushrooms, mozzarella shreds, and brussels sprouts. Serve pizzas alongside remaining garlic ranch, or reserve for another use.
Dough can be chilled up to 24 hours. Garlic ranch can be made up to 3 days in advance and stored in an airtight container in refrigerator.
For scratch-made pizza dough, find our Artisan Pizza Dough recipe here.
Earthy Italian white: Garofoli Podium Verdicchio