Preheat the oven to 300°F, and adjust a rack to the center.
Do not peel the onions! Slice the root end off of each one, just about 1/2-inch — only enough to create a base so the onions don’t roll around. Then slice about 1-inch off the tip end of each one, and use the knife to mark an “X” on top, going in only 1/2-inch or so. Place them in a 9 x 13 x 2-inch pan, root ends down.
Drizzle the onions evenly with about 2 tablespoons of the oil and sprinkle generously with salt and pepper.
Place in the preheated 300°F oven, uncovered. After 1 hour, remove them from the oven and drizzle with another 2 tablespoons of the oil, and the vermouth divided among them. Then cover the pan lightly with foil, return them to the oven for 1 more hour.
Remove from the oven again and take off the foil. Add about half of the fresh herb sprigs to the pan, surrounding the onions. Then drizzle the onions evenly with the remaining oil and insert about 1/2 tablespoon of butter into the center of each onion and turn the oven up to 350°F. Return the onions, uncovered, to the preheated 350°F oven and roast for another 30 minutes.
Remove from the oven and let them cool in the pan. Once they’re cool enough to touch, take off the skins, slice and serve with the remaining fresh herbs.