Bring a large pot of well-salted water to a boil. Combine the oil and garlic in a 12-inch skillet over medium-low heat. Cook, stirring often, until the garlic becomes fragrant and is just beginning to turn golden, 4 to 6 minutes. Add the spinach, 1/2 tsp. salt, and 1/4 tsp. pepper and cook, tossing gently with tongs, until the spinach begins to wilt, 2 to 3 minutes more. Remove from the heat. Meanwhile, cook the spaghetti in the boiling salted water, stirring occasionally, until it’s just tender to the tooth (see the package for cooking time). Reserve 1 cup of the cooking water and drain the pasta. Return the skillet to medium heat. Add the drained pasta and 1/2 cup of the reserved cooking water. Cook for 1 to 2 minutes, tossing and stirring to combine and blend the flavors. If the pasta isn’t tender or seems dry, add the remainder of the cooking water and continue to cook and stir until done. Toss with the cheese. Season to taste with salt and pepper and serve immediately.