Sunchokes, also known as Jerusalem artichokes, are a knobby tuber that look similar to a potato, but taste reminiscent of an artichoke.
Preheat the oven to 425°F. Line two baking trays with parchment paper.
In a large bowl, combine the sunchokes, potato, garlic, and 1 tablespoon oil, season with salt and pepper, and toss together. Transfer to one of the baking sheets, arranging the vegetables in a single layer. In the same bowl, toss the mushrooms with another tablespoon of oil, lightly season with salt and pepper, and transfer to the other baking sheet, then set aside.
Bake the sunchoke-potato mixture for 20 minutes, then add the tray of mushrooms and continue to bake both trays for an additional 20 to 25 minutes, until the sunchokes and potatoes are tender and starting to caramelize. Remove both trays from the oven and set aside to cool.
In a large saucepan or Dutch oven, heat the remaining 2 tablespoons oil over medium-high heat. Add the onion and shallot plus a pinch of salt, and sauté until translucent and starting to brown, approximately 10 to 12 minutes. Add the sage, thyme, and salt, and cook for an additional minute or two. Add the wine and stir well, scraping up any browned bits, then allow to cook for 5 minutes more, until the wine is slightly reduced. Finally, add the roasted vegetables and 6 cups of vegetable stock, then bring to a boil. Cover, reduce the heat, and simmer for 20 minutes.
Uncover the soup and allow it to cool slightly, then blend in batches, filling the blender container no more than halfway and covering the top of the blender with a folded kitchen towel to protect your hands from steam. (Alternatively, use an immersion blender, but be aware that the texture of the soup won’t be quite as smooth.) Add additional vegetable stock if necessary to thin the soup, then add the lemon juice, salt, and pepper to taste. Reheat over medium heat, ladle into bowls, and drizzle with olive oil. Serve hot.