Place the 2 peeled whole garlic cloves, 2 teaspoons of the grated ginger, and the water in a blender. Blend until smooth, about 25 seconds; leave the mixture in the blender jar and set aside. (You will be pureeing the soup right in the blender with the garlic and ginger.).
Heat the butter in a large stockpot or Dutch oven over medium heat until foaming. Add the onions, peppers and tomato paste, stirring frequently, until the onions are softened and beginning to brown, about 3 minutes. Stir in the coconut and cook until fragrant, about 1 minute. Add the minced garlic, remaining 2 teaspoons ginger, curry powder, cumin, chili flakes, and flour; stir until evenly combined, about 1 minute. Whisking constantly and vigorously, gradually add the chicken broth.
Add the carrots, celery, and whole banana to the pot. Increase the heat to medium-high and bring to a boil. Add the chicken, cover, reduce the heat to low, and simmer until the vegetables are tender and the chicken is cooked through, about 20 minutes. With tongs, transfer the cooked chicken to a cutting board, cool slightly, and pull into bite-sized pieces.
Puree the soup in batches in the blender with the garlic and ginger until very smooth. Wash and dry the pot. Return the pureed soup to the clean pot, add the reserved chicken, and season to taste with salt and pepper. Warm the soup over medium heat until hot, about 1 minute. (The soup can be refrigerated in an airtight container for up to 3 days. Warm over low heat until hot; do not boil.) sprinkle with the cilantro, and serve immediately.