Fill a large pot with water and bring to a boil. Add the 3 cups baby spinach and blanch for 1 minute, then remove with a slotted spoon into a bowl of ice water to stop cooking.
Drain the spinach from the ice water, lay on paper towels, squeeze out excess water, and set aside.
Add a generous pinch of salt to the boiling water and cook 1/2 pound dry fettuccine until al dente according to package instructions. Reserve 1 cup pasta cooking water, then drain the pasta.
Meanwhile, heat a large sauté pan over medium heat and melt 4 tablespoons unsalted butter. Add the minced shallot and sauté until tender, about 5 minutes.
Pour in 1 cup heavy whipping cream and bring to a boil, stirring occasionally. Cook until the sauce begins to thicken.
Season the sauce with 1/4 teaspoon freshly ground nutmeg, 1/2 teaspoon salt, and ground black pepper to taste. Taste and adjust seasoning if needed.
Add the drained pasta, about 1/2 cup of the reserved pasta water, and the squeezed spinach to the pan. Toss and cook over medium heat for 3–4 minutes until the sauce coats the pasta, adding more pasta water if needed to reach desired consistency.
Remove from heat and toss in the 1/4 cup basil strips. Serve with additional basil and freshly ground black pepper if desired.