Melt butter in a large pot (at least 5 qts.) over medium-high heat, then add onions. Cook until onions are translucent, 5 to 7 minutes. Add garlic, carrots, bay leaf, rice, 2 tsp. salt, pepper, and chicken broth.
Increase heat to high and bring to a boil, then reduce to medium-high and cook, uncovered, until carrots are tender, about 20 minutes. Remove from heat and let cool 10 minutes.
Remove bay leaf and purée soup in batches in a blender. Return soup to pot and set over low heat. Add whipping cream and 2 cups water (if soup looks too thick, add a little more water) and cook until warmed through. Season to taste with additional salt.
Serve soup hot, with crème fraîche or sour cream, dill, and tarragon.
Note: Nutritional analysis is per cup.