Preheat oven to 400 degrees F.

DO NOT PEEL THE ONIONS. Cut onions almost in half, leaving the root ends intact. Pry each open slightly to expose the cut sides. Place the onions root side down in a foil-lined roasting pan and roast until just beginning to soften and brown, 75-90 minutes. Check them frequently.

Just before the onions finish cooking, melt the butter in a small saucepan and cook, swirling occasionally, until the butter is brown and smells nutty, 5-8 minutes. Let cool slightly. Whisk in the vinegar and season the brown butter with salt.

Divide the onions among the diners, leaving the skin on. Spoon brown butter over.

Goes well with a side dish containing meat or strong vegetables.