Preheat the oven to 350 degrees F.
Place the onion on a large piece of aluminum foil. Drizzle the onion with 2 tablespoons of the olive oil and season with salt and pepper. Wrap the onion tightly in the foil and roast until tender and lightly golden brown, about 50 minutes to 1 hour.
Remove from the oven and cool. When cool, roughly chop the onion and place in the bowl of a food processor. Process until smooth. With the machine running, slowly add the remaining 1/4 to 1/2 cup olive oil through the feed tube, until the dressing is smooth. Season with salt and pepper.