Place ¼ cup extra-virgin olive oil in small bowl. Place 1 pound room-temperature pizza dough on lightly floured counter, pat dough into rough 8-inch square, and cut into 32 pieces (½ ounce each). Working with 1 piece of dough at a time, roll into tight ball. Roll each dough ball in oil to coat before evenly spacing 18 balls around edge of 12-inch cast-iron skillet, keeping center of skillet clear. Continue rolling dough balls in oil and place remaining 14 balls on top of first layer, staggering them between seams of balls underneath. Cover loosely with greased plastic wrap and let sit until slightly puffed, about 20 minutes.

Whisk 8 ounces softened cream cheese, ¾ cup jarred pizza sauce, 1 minced garlic clove, ½ teaspoon dried oregano, and ¼ teaspoon red pepper flakes until thoroughly combined. Stir in 4 ounces shredded whole-milk mozzarella cheese (1 cup); 3 ounces pepperoni, cut into ¼-inch pieces; 1 ounce Parmesan cheese, grated (½ cup), and 4 tablespoons scallions; set aside.

FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter mounded with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour into steeply banked pile against side of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.

FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave primary burner on high and turn off other burner(s). (Adjust primary burner as needed to maintain grill temperature of 425 to 475 degrees; if using 3-burner grill, adjust primary and secondary burner).

Melt 3 tablespoons unsalted butter in small saucepan set over hotter side of grill. Add ⅛ teaspoon table salt, remaining 3 minced garlic cloves, and remaining ⅛ teaspoon pepper flakes. Cook until just fragrant, about 1 minute. Set aside.

Remove plastic from cast-iron skillet. Transfer skillet to cooler side of grill, cover grill, and cook until rolls are just beginning to brown, about 20 minutes, rotating skillet halfway through baking.

Off heat, spoon cream cheese mixture into center of skillet. Return skillet to cooler side of grill, cover grill, and bake until dip is heated through and rolls are golden brown, 10 to 15 minutes. Brush bread with reserved butter mixture. Sprinkle dip and rolls with Parmesan as desired, then top dip with remaining scallions. Serve.