Melt the butter in a large saucepan over medium heat. Stir in the onions, crystallized ginger, fresh ginger, garlic, salt, and sugar. Cook, stirring often, until the onions are softened and translucent but have not yet begun to brown, about 5 to 7 minutes.

Stir in the carrots, water, half of the carrot juice (3/4 cup), thyme sprigs, and baking soda. Increase the heat to high and bring the liquid to a simmer, then reduce the heat to medium-low. Cover and simmer gently until the carrots are very tender and yield easily to a fork, 20 to 25 minutes.

Discard the thyme sprigs. Working in batches, process the soup in a blender until completely smooth and velvet-like, 1 to 2 minutes per batch. Return the pureed soup to a clean pot and stir in the vinegar and the remaining carrot juice.

Return the soup to a brief simmer over medium heat to meld the flavors. Season with salt and pepper to taste and serve immediately, garnishing each bowl with a dollop of sour cream and a sprinkle of chives.