Bring a large pot of salted water to boil and add the spaghetti. Cook until al dente, reserving 1 cup of pasta cooking water before draining.
Meanwhile, heat the olive oil in a large (3-quart) saucepan over medium heat until shimming. Add the garlic, parsley, red pepper flakes, and 1/4 cup of water. Cover and sweat, stirring occasionally, until soft, adding more water if necessary to keep the garlic from caramelizing too much.
Add the cooked pasta to the garlic mixture and toss well to combine. Add some pasta cooking water if necessary to bring the dish to a creamy consistency. Serve with more olive oil and the minced tops of the green garlic, if desired.