In a medium bowl, cover the dried mushrooms with warm water by 3 inches. Place a small plate on top of the mushrooms to keep them submerged, then let them soak until softened, about 30 minutes.
Remove the mushrooms from the water, squeezing them lightly to remove as much water as possible. Rinse them under cool water to remove any grit. Set aside.
Heat a large, heavy-bottom pot over medium heat. Add the butter and shallots, reduce the heat to medium-low, and cook, stirring occasionally, until the shallots are soft and translucent, about 10 minutes.
Add the fresh and dried mushrooms, half of the thyme, and all of the garlic powder and cook, stirring often until the mushrooms have released their juices and almost all of the liquid has evaporated, about 20 minutes.
Increase heat to medium. Add 1/4 cup of the chicken broth and stir, scraping the pot to free up any browned bits. Cook until the broth is reduced and the pan is mostly dry, 1 to 2 minutes. Season with the salt and pepper. Add the cream and half and half and heat, stirring occasionally, until small bubbles form around the pot’s edges, 5 minutes. Working in batches, puree the mushroom soup in a blender until smooth. Pour the pureed batches into a fresh saucepot and whisk in the remaining chicken broth and the apple cider vinegar.
Season to taste, ladle into bowls, garnish each serving with 1 tablespoon sour cream and a sprinkle of the remaining fresh thyme, and serve.