6oz. Mixed Mushrooms, cut or torn into large pieces (about 3½ cups)
2 tbsp. Extra-Virgin Olive Oil, plus more for drizzling
1 lb. store-bought Pizza Dough, room temperature
⅓ cup (or more) Barbecue Sauce
6 oz. Fresh Mozzarella, torn (about 1 cup)
2 oz. Smoked Gouda, coarsely grated (about ½ cup)
½ small Red Onion, thinly sliced
Kosher Salt and Freshly Ground Pepper
Crushed Red Pepper Flakes and Cilantro leaves (for toppings)
Place a rack in upper third of oven and preheat to 475°. Drizzle 6 oz. mixed mushrooms, cut or torn into large pieces (about 3½ cups), with extra-virgin olive oil in a large bowl; toss to coat. Set aside.
Swirl 2 Tbsp. extra-virgin olive oil in a 12" cast-iron skillet to coat bottom and ½" up sides. Place 1 lb. store-bought pizza dough, room temperature, in pan; lift, stretch, and press dough so it fills pan. If dough shrinks from edges, cover with a kitchen towel and let rest 10 minutes before stretching again.
Bake just until crust is starting to set but hasn’t taken on any color, about 5 minutes. Carefully remove skillet from oven and spread ⅓ cup barbecue sauce over entire surface of crust. Top with 6 oz. fresh mozzarella, torn (about 1 cup), and 2 oz. smoked Gouda, coarsely grated (about ½ cup), followed by ½ small red onion, thinly sliced, and reserved mushrooms. Season with kosher salt and freshly ground pepper.
Return skillet to oven and continue to bake until crust is golden brown underneath, cheese is melted, and mushrooms are golden, 16–20 minutes longer.
Heat broiler. Broil pizza until mushrooms are browned and crispy and cheese is browned in spots and bubbling, about 2 minutes. (Begin checking after 1 minute.)
Drizzle more barbecue sauce over pizza if desired. Top with crushed red pepper flakes and cilantro leaves.