In a 4-quart stockpot over medium-high heat, add butter and oil. Once butter is melted add onions and celery. Cook until onions are translucent, about 3-4 minutes. Add ginger and garlic to the pot and cook for about 30 seconds. Add the carrots, stirring occasionally, until carrots are slightly caramelized, 7-8 minutes. Add stock, salt, pepper, and bay leaf, bring to a boil and then reduce heat to a simmer. Cook for 20-25 minutes until carrots are soft.
Remove the stockpot from burner and take the bay leaf out. Using an immersion blender, puree soup. (You can also let soup cool and puree in a food processor or blender.)
Add more salt and pepper to taste. Stir in 3/4 cup yogurt. Return to burner and reheat over medium. Ladle into serving bowls and garnish with remaining yogurt and chopped chives.