Bring a large pot of water to a rolling boil. Add the baby spinach and blanch for 1 minute, then remove with a slotted spoon and transfer to a bowl of ice water to stop cooking.
Drain the spinach from the ice water, gently squeeze out excess water using paper towels, and set aside.
Add a generous pinch of salt to the boiling water and cook the fettuccine until al dente according to package directions. Reserve 1 cup of the pasta cooking water, then drain the pasta.
While the pasta cooks, melt the butter in a large sauté pan over medium heat. Add the minced shallot and sauté until tender, about 5 minutes.
Pour in the heavy whipping cream and bring to a gentle boil, stirring occasionally, until the sauce begins to thicken.
Season the sauce with nutmeg, 1/2 teaspoon salt, and freshly ground black pepper to taste. Adjust seasoning if needed.
Add the drained pasta, about 1/2 cup of the reserved pasta water, and the blanched 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 necessary to reach desired consistency.
Remove from heat and toss in the basil strips with tongs. Serve immediately with additional basil and a grind of black pepper if desired.