1/4 cup extra-virgin olive oil, plus more
1/3 cup pine nuts
4 small onions, unpeeled
1/4 cup drained capers
1/4 cup raisins
1/4 cup red wine vinegar
8 whole red mullets or 4 red snappers, scales removed, cleaned
1 cup parsley leaves with tender stems
Aleppo-style or other mild red pepper flakes and lemon wedges (for serving)
Preheat oven to 350°F and prepare a grill for medium-high heat. Clean grate well with a brush; oil grate. Toast pine nuts on a rimmed baking sheet, tossing once, until golden brown, about 5 minutes. Let cool (that’s it for the oven).
Grill onions, turning occasionally, until skins are blackened and onions have softened (some of the juices may ooze out), 15–20 minutes. Transfer to a platter and let cool 10 minutes.
Split onions in half. Remove outer peel and discard. Separate onion layers into individual petals. Transfer to a medium bowl and mix in pine nuts, capers, raisins, and vinegar; season agrodolce with salt.
Season fish cavity and skin with salt; drizzle with 1/4 cup oil. Grill, resisting the urge to turn, until skin is lightly charred and flesh is flaky and opaque down to the bone, about 3 minutes for mullet and 8 minutes for snapper. Place a metal spatula underneath fish, then lift and gently roll over onto the other side. Cook until flesh is flaky and opaque, 3–8 minutes, depending on fish. If a small knife slides easily through the thickest part of flesh, fish is done.
Transfer fish to a platter and spoon agrodolce over. Top with parsley and some red pepper flakes; drizzle with oil. Serve with lemon wedges.