6 tablespoon (90ml) extra-virgin olive oil, divided
1 ¼ pounds (565g) onions (2 large), halved lengthwise and thinly sliced
14 to 16 ounces (395g-450g) pizza dough, thawed if frozen
¼ pound (115g) Gorgonzola dolce, crumbled (1 cup)
½ cup (125ml) walnuts, toasted and coarsely chopped
¼ cup (50ml) chopped flat-leaf parsley
Heat ¼ cup (50ml) oil in a 12-inch (30mm) heavy skillet over medium-low heat until it shimmers, then cook onions with ½ tsp (2ml) salt and ¼ tsp (1ml) pepper, covered, stirring occasionally, until golden, 15 to 20 minutes. Transfer to a small bowl and keep warm, covered.
Prepare a grill for direct-heat cooking over low charcoal (medium heat for propane).
Stretch dough into a roughly 12 (30mm)- by 10-inch (25mm) rectangle on a large baking sheet and brush with 1 Tbsp oil (15ml).
Bring dough, onions, cheese, nuts, parsley, and remaining Tbsp oil to grill area.
Oil grill rack, then put dough, oiled side down, on grill and brush top with remaining Tbsp oil. Grill, covered, until underside is golden brown, 1 ½ to 3 minutes.
Using tongs, return crust to baking sheet, turning crust over (grilled side up). Sprinkle evenly with onions, cheese, nuts, and parsley. Slide pizza from sheet on to grill and grill, covered, until underside is golden brown and cheese is partially melted, about three minutes. Transfer to a cutting board and cut into pieces.