In a large oven-proof skillet, melt the butter over medium heat. Add the shallots, flat side down.
Cook, turning occasionally, until the shallots are browned, about 10 minutes.
Remove the pan from the heat and let it slightly cool. Drizzle the vinegar on top of the shallots, then sprinkle them with kosher salt and black pepper. Toss the shallots to coat them in the pan liquids.
Transfer the skillet to the oven. Roast the shallots for 10 minutes, flat side down. Carefully turn them to the other side and keep roasting until they are deeply browned and fork-tender (and smell amazing!), about 10 more minutes.
Divide the shallots between plates, spoon the pan sauce on top, and serve. You can garnish them with parsley if you wish.
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Notes
Leftovers keep well in the fridge, in an airtight container, for 3-4 days. Gently reheat them in the microwave on 50% power prior to serving.This is one of those recipes where the leftovers truly taste good - almost as good as the freshly made dish. I sometimes chop them up and mix them into an omelet the next day for my breakfast, with a bit of shredded gruyere cheese. Yum!