How to Make It
Bring a large pot of salted water to a boil. Add the spaghettini and cook until al dente. About 30 seconds before the spaghettini is done, add the spinach to the pot. Drain the spaghettini and spinach, reserving 1/4 cup of the pasta cooking water. Return the pasta and spinach to the pot.
Meanwhile, in a large skillet, heat the olive oil. Add the garlic and cook over moderate heat until golden, about 8 minutes. Add the cream and thyme and simmer over low heat until the garlic is tender, about 5 minutes. Remove from the heat. Whisk in the 1/3 cup of Parmigiano-Reggiano and season with salt and pepper.
Add the garlic cream to the pasta along with the reserved pasta cooking water and toss well. Season with salt and pepper. Transfer the pasta to bowls and serve, passing extra grated cheese at the table.