Bring a large pot of aggressively salted water to a boil. Cook spaghetti until al dente. Reserve 1 ½ cups of the starchy pasta water, then drain.
While the pasta cooks, heat the olive oil gently in a large skillet over medium-low. Add the garlic slices and whole parsley stem, stir constantly until the garlic turns light golden… not brown (about 3 minutes).
Stir in the chili flakes and a pinch of salt. Let them bloom for 30 seconds, then remove the parsley stem and take the pan off the heat.
Add about ½ cup of the reserved pasta water to the skillet and stir/whisk vigorously to combine with the oil. It'll start looking creamy and slightly thick… that's your emulsion forming.
Return the pan to medium-low heat and add the drained spaghetti along with another splash of pasta water. Toss everything aggressively with tongs for 1–2 minutes, drizzling in 1 to 2 more tablespoons of olive oil and a bit more pasta water as you go. Alternate between the two while tossing nonstop. The sauce should turn silky and glossy. If it looks dry or clumpy, add more water; if it looks thin, keep tossing.
Turn off the heat and stir in the chopped parsley. Taste and add a tiny pinch of salt if needed.
Plate immediately, spooning any extra sauce from the pan over the top. Garnish with lemon zest and a sprinkle of Parmesan if you'd like.
