To make Basic Dashi:
Put the water, kombu, and shiitake in Big Deal (or another stockpot) and soak for 24 hours before making the dashi.
Heat kombu, shiitake, and water over low heat, aiming for about 140 degrees F. Continue to cook on low heat for an hour. Remove shiitake and kombu. Add bonito flakes and simmer for 30 minutes. Strain through a fine mesh strainer, pressing the solids to get maximum flavor.
To make Barley-Miso Soup:
Combine everything in The Dutchess (or any Dutch oven) and heat over medium-low heat. Once warm, blend with an immersion blender or whisk (using a blender ensures a smoother texture).
Add clams to the broth and cover with lid. Cook until clams have opened. Discard any unopened clams.
Add the cubed tofu, garnish with scallions and serve warm. Be sure to stir in between servings to ensure everything is mixed well.