Cook the pasta. Prepare the pasta according to the package directions.
Sauté the garlic. Melt the butter over medium heat in a large skillet or Dutch oven. Add garlic and continue to stir and cook until fragrant, about 30 seconds.
Add the spinach. Stir in the spinach, season with salt, pepper, and basil, and cook until wilted, about 1 to 2 minutes. Depending on the size of your skillet, you might have to cook the spinach down in batches.
Combine. Drain the cooked pasta and add it to the spinach mixture; add the cream cheese and milk. Mix, then continue cooking and stirring until everything is well incorporated and the cream cheese is melted.
Finish and serve. Taste the pasta for seasonings and adjust accordingly. Top with fresh Parmigiano-Reggiano shavings, and serve.