Step 1

In a pot, cover potatoes with 2 inches water; generously season with salt. Bring to a boil over high heat; cook 8 minutes. Add onions; continue boiling until potatoes are easily pierced with the tip of a knife and onions are crisp-tender, 4 to 5 minutes more. Drain; let cool slightly. When cool enough to handle, peel onions.

Step 2

Preheat grill to medium-high. In a wide, shallow dish, whisk together vinegar, mustard, and 1/2 cup oil. Chop enough oregano to yield 3 tablespoons (from 2 to 3 sprigs) and stir into vinaigrette with olives; season with salt and pepper. In another bowl, toss potatoes and onions with remaining 1 tablespoon oil; season with salt and pepper. Brush fish and remaining oregano sprigs with oil; season with salt and pepper.

Step 3

Brush grates with oil, add vegetables, and grill, turning a few times, 6 minutes. Add fish to grill and top with oregano. Cook fish and vegetables, turning fish once halfway through, until fish is just cooked and vegetables are charred in places and tender, 8 to 10 minutes more. Transfer to dish with vinaigrette, turning to evenly coat. Let stand, turning a few times, until no longer hot but still warm, 10 minutes. Meanwhile, grill split side of bread until charred in places, 1 to 2 minutes; slice. Serve fish, vegetables, and vinaigrette over greens, with grilled bread.