Bring a large pot of water to a rolling boil.
Add the baby spinach to the boiling water 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, lay on paper towels, squeeze out excess water, 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.
Meanwhile, heat a large sauté pan over medium heat and melt the butter.
Add the minced shallot and sauté until tender, about 5 minutes.
Pour in the heavy whipping cream, bring to a gentle boil, and cook, stirring occasionally, until the sauce begins to thicken.
Season the sauce with nutmeg, 1/2 teaspoon salt, and ground black pepper to taste; adjust seasoning if needed.
Add the drained pasta, 1/2 cup of the reserved pasta water, and the squeezed spinach to the sauce; toss and cook over medium heat 3–4 minutes until the sauce coats the pasta, adding more pasta water if needed for desired consistency.
Remove from heat and toss in the basil strips with tongs.
Serve immediately with additional basil and freshly ground black pepper if desired.
