Step 1

Place 1 small red onion, thinly sliced, in a small heatproof bowl. Toast 2 Tbsp. coriander seeds in a dry small saucepan over medium-high heat, tossing often, until fragrant and slightly darkened in color, about 2 minutes. Add ⅓ cup distilled white vinegar, 1 Tbsp. sugar, and 1 Tbsp. water and bring to a boil, stirring to dissolve sugar. Strain liquid through a fine-mesh sieve over onion; discard solids. Season liberally with kosher salt and stir to combine. Let cool.Do Ahead: Red onion can be pickled 3 days ahead; cover and chill. Bring to room temperature before using.

Step 2

Heat 2 Tbsp. extra-virgin olive oil in a medium saucepan over medium. Cook ½ medium white onion, coarsely chopped, stirring occasionally, until softened, about 5 minutes. Add 2 garlic cloves, coarsely chopped, season with kosher salt, and cook, stirring occasionally, until garlic is softened and onion and garlic are golden brown around edges, about 5 minutes. Pour in 3 Tbsp. vodka and cook, stirring and scraping bottom of pan with a wooden spoon, until evaporated, about 1 minute. Stir in one 14-oz. can crushed tomatoes and cook, stirring occasionally, until thickened, 14–16 minutes.

Step 3

Transfer sauce to a blender, add ⅓ cup cashew milk or heavy cream, and blend until smooth. Add ⅓ cup finely grated Pecorino Romano and a pinch of crushed red pepper flakes; blend until incorporated.Do Ahead: Sauce can be made 3 days ahead. Let cool; cover and chill.

Step 4

Prepare a grill for medium-high heat; oil grate with vegetable oil. (Alternatively, heat an oiled cast-iron grill pan over medium-high.) Pat 2 skin-on, boneless chicken thighs dry with paper towels. Toss with 1 tsp. vodka and 2 tsp. vegetable oil in a small bowl; season with kosher salt. Grill until lightly charred and cooked through, 3–4 minutes per side. Transfer to a cutting board and let cool slightly. Slice chicken and set aside.

Step 5

If using a conventional oven: Heat broiler. Heat 2 tsp. extra-virgin olive oil in a 12" cast-iron skillet over medium. Using lightly oiled hands, flatten 1 ball All-Purpose Pizza Dough or 12 oz. store-bought pizza dough, room temperature and gently stretch over the backs of your hands to create a 12" round. Transfer to skillet, stretching to edges of pan if needed, and cook until bottom is golden brown, about 4 minutes. Transfer skillet to oven and broil until crust is beginning to char in spots, about 2 minutes.

Step 6

Carefully remove skillet from oven (handle will be hot!). Ladle about ½ cup sauce onto center of dough (save remaining sauce for another use) and spread over crust, leaving a 1" border. Top pizza with 3 oz. fresh mozzarella, torn and reserved chicken; season with salt. Return to oven and continue to broil until cheese is melted and crust is charred in spots, about 1 minute longer.

Step 7

If using a pizza oven: Preheat to high. Lightly flour your hands and a pizza peel. Working from the center outward, stretch out dough on peel to a 12" round. Ladle about ½ cup sauce onto center of dough and spread over crust, leaving a 1" border. Top with 3 oz. fresh mozzarella, torn and reserved chicken; season with salt. Slide pizza into oven and cook, rotating occasionally, until cheese is melted and crust is charred in spots, 2–3 minutes.

Step 8

Toss ¼ cup (packed) baby arugula with 1 tsp. fresh lemon juice in a small bowl; season with salt.

Step 9

Top pizza with drained pickled red onion, Pecorino Romano, and arugula. Season with freshly ground black pepper.