Heat oil in medium saucepan over medium heat. Add onion and carrot and cook until carrots soften, about 5 minutes. Add garlic and cook 1 minute. Add bell peppers, broth, and paprika, and bring to a boil over high heat.
Tie thyme and parsley sprigs with kitchen string or a clean twist tie and drop into soup along with potatoes. Reduce heat to medium-low and simmer until potatoes are tender, 15 to 20 minutes.
Remove thyme-parsley bundle and transfer soup to a blender or food processor (in batches, if necessary). Add pomegranate juice, orange juice, salt, and pepper. Puree soup until very smooth, about 2 minutes. Rewarm over low heat, then remove from heat and stir in sour cream. Ladle into bowls and garnish each serving with a few drops of pomegranate juice. Serve with toasted Panera Bread Tomato Basil Bread.
Tip: Buy roasted red bell peppers at your grocery store’s salad bar. Or look for them in jars in the Italian food section. For more smokiness, add a few drops of liquid smoke, which is stocked near the barbecue sauce in most grocery stores.