Melt butter in a medium frying pan over medium heat. Add minced shallot and 3/4 cup green onions and cook, stirring often, until softened and fragrant, 4 to 5 minutes.

Add the wine, increasing heat to medium-high, and cook down until nearly evaporated, about 1 minute. Stir in the cream, parmesan cheese, nutmeg, and 1 tsp. each salt and pepper. Bring to a simmer, reduce heat to medium-low, and cook until cream is slightly thickened, about 3 minutes.

Cook pasta according to package instructions until just tender, about 8 minutes. Reserve 1 cup cooking water, then drain pasta.

Add the shrimp to cream sauce, increasing heat to medium, and cooking shrimp just until pink, 4-5 minutes. Add pasta to frying pan and gently mix together. Stir in reserved pasta water (mixture will be soupy, then thicken as it stands) and toss in the rest of the green onions. Add more salt and pepper if you like.

Serve right away!