Preheat a griddle or cast-iron skillet. Brush sweet onion slices with olive oil and season with salt and pepper. Place on griddle and cook, turning once, until tender, 4 to 5 minutes. Remove onions from griddle and separate into rings.
Place grilled onions in a large bowl along with, lettuce, fennel, roasted peppers, tomatoes, cucumber, scallions, red onion, dill, parsley, oregano, olives, and caperberries; toss to combine.
Drizzle salad with vinaigrette and toss until vegetables are well coated. Top with feta and add pepperoncini; serve.