Step 1Heat the oven to 400 degrees. Peel one of the onions but leave it whole. Rub 1 tablespoon of the oil and a pinch each of the salt and pepper over the onion, then wrap it in foil. Roast the onion until it is softened and lightly caramelized, about 1 hour. Remove and cool.
Step 2Meanwhile, peel and chop the remaining onion.
Step 3Heat a medium, heavy-bottom saucepan over medium heat. Add the remaining olive oil and a pinch each of salt and pepper. Stir in the chopped onion, carrot and celery and cook until softened, about 8 to 10 minutes. Stir in the garlic, shallots and mushrooms and cook for 5 minutes, stirring frequently. Reserve one mushroom to garnish the finished soup.
Step 4Stir in the wine, making sure to scrape the browned bits from the bottom of the pan. Stir in the fresh thyme and bring the contents to a gentle simmer. Cook until the mushrooms soften, about 5 to 6 minutes. Stir in the vegetable stock and continue to simmer until the liquid is reduced by half, about 10 minutes.
Step 5Remove from the heat and puree the soup with an immersion blender, or in batches in a blender. Return the soup to low heat and stir in the cream. Season with a generous teaspoon of salt and a pinch of pepper, or to taste. This makes about 8 cups of soup.
Step 6Chop the roasted onion into pieces no larger than one-quarter inch. Stir the chopped onion into the soup. Check and adjust the seasoning if desired.
Step 7Slice the reserved mushroom into 8 very thin, lengthwise slices. Ladle the soup into warmed bowls. Garnish each portion with a thin shaving of the Parmigiano-Reggiano, one-fourth teaspoon of the chives and a thin slice of mushroom. Serve immediately.