Preheat a grill or broiler. Bring a large pot of water to a boil.
Meanwhile, melt the butter in a large skillet or saucepan over medium heat. Put the shrimp in a bowl and drizzle about one-third of the butter over them. Toss to coat them and set aside.
Add the shallots to the remaining butter and sauté until tender, 2 to 3 minutes. Add the champagne and raise the heat to high. Put the ginger in a garlic press and press it over the skillet or pan, letting its juices drip into the pan; alternatively, grate the ginger into the pan. Boil the champagne briskly until it reduces by one-half, 5 to 7 minutes.
Add the cream to the reduced champagne and continue boiling until thick and reduced by one-fourth to one-third, about 10 minutes more.
As soon as you add the cream to the champagne, put the pasta in the boiling water and cook until al dente, following the manufacturer's suggested cooking time.
Season the shrimp lightly with salt and white pepper and grill or broil them until they turn pink, opaque, and lightly golden but still juicy, about 2 minutes per side.
As soon as the pasta is done, drain it and toss with the sauce. Arrange in individual serving plates or bowls and top with the grilled shrimp. Garnish with the salmon roe or golden caviar and the shredded nori and serve immediately.