In a saucepan, combine the water and kombu over medium-high heat and bring to a simmer. Adjust the heat to maintain a low simmer and cook for 20 minutes. Remove the pan from the heat and add the bonito flakes. Cover the pot and let stand for 10 minutes.

Strain the liquid through a fine-mesh sieve placed over a clean saucepan and discard the contents of the sieve. Add the potatoes, place the pan over medium-high heat and bring to a boil. Reduce the heat to medium-low, cover and simmer until the potatoes are tender when pierced with the tip of a paring knife, about 40 minutes.

Just before the potatoes are ready, in a small saucepan, bring the cream to a simmer over medium heat.

Drain the potatoes, discarding the liquid. Pass the potatoes through a potato ricer into a small saucepan. Add the cream and whisk well to incorporate. Place over low heat and stir until the mixture is smooth. Whisk the 2 tablespoons Seaweed Butter into the potato-cream mixture until well blended, and then add the salt. At this point, transfer the potatoes to the desired serving vessel. This can be served family-style in a large serving bowl, or as a side dish in individual bowls. Using a mandoline, finely shave several pieces of the frozen seaweed butter and place a few pieces on top of the potatoes. Using a grater, grate a little of the bonito over the top. Serve right away.

Put the seaweed in the blender and process on high speed until broken into fine pieces, 30 to 45 seconds. Transfer the seaweed to a large bowl and rinse under cold running water until fully hydrated, about 10 minutes. Drain the seaweed, return it to the blender, add the butter and process until fully blended. Divide the butter in half and transfer each half to a large sheet of plastic wrap. Roll the butter up in the plastic wrap pieces, forming two thick logs. Refrigerate one half and freeze the other. It will keep for up to 2 weeks.