Melt the butter in a large heavy-bottomed pot over medium-high heat. Add the carrots, parsnips, garlic, turnips, onion, rutabaga, ginger, allspice, coriander and some salt and pepper. Stir and sauté for about a minute, until the vegetables are all coated in butter and starting to cook. Add the stock and thyme sprigs. Bring to a boil, reduce to a strong simmer and cook until the vegetables are tender, about 20 minutes.
While the soup is cooking, heat the vegetable oil in a large skillet. Add the shallot slices and fry until golden brown, about 5 minutes. They will crisp as they cool. Drain on paper towels and salt them while they are still hot.
Puree the soup with an immersion blender or carefully in batches using a standard blender. Serve the soup hot, garnished with the fried shallots and parsley.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.