Heat the extra-virgin olive oil in large Dutch oven over medium-high heat. Add the onions, garlic, ginger and chile pepper and sweat them out a few minutes. Stir in the carrots and tamari sauce, then cover the pot and cook for 7 to 8 minutes. Add the stock and bring to a boil. Reduce the heat and simmer the soup until the carrots are tender. Puree as smooth or chunky as you like with hand blender or in a processor, in batches. Season the soup with salt and pepper, to taste. Cool completely and store in the refrigerator for a make-ahead meal.
Reheat, in a covered pot, over medium heat and serve in shallow bowls with a fried egg on top, cooked to your liking. Garnish each serving with chives or scallions and a drizzle of toasted sesame oil on top. Pass the toasted sesame rolls at the table, for dunking.