Salt your water generously. Bring a large pot of water to a rolling boil and add enough salt so it tastes like the sea. This is the first and best chance to season your spaghetti from within.
Cook the pasta. Add the spaghetti and cook until just shy of al dente, typically 1–2 minutes less than package instructions.
Stir occasionally so it doesn’t stick.
Reserve pasta water. Before draining, scoop out about 1½ cups of the starchy cooking water. You’ll use this to build the sauce.
Melt butter and warm the oil. In a large skillet over medium heat, melt the butter with the olive oil. The oil raises the butter’s smoke point and helps the sauce stay silky.
Sauté the garlic gently. Add the sliced garlic and cook for 1–2 minutes, stirring, until fragrant and just turning pale gold.
Keep the heat moderate so it doesn’t burn.
Bloom the heat. Sprinkle in the red pepper flakes and let them toast for 20–30 seconds. This wakes up their flavor and perfumes the sauce.
Build the emulsion. Add a generous splash (about ½ cup) of reserved pasta water to the skillet and swirl. It will look loose at first; that’s perfect.
Toss in the pasta. Add the drained spaghetti to the skillet.
Toss vigorously so every strand is coated. Add more pasta water as needed to create a glossy, clinging sauce.
Season and enrich. Add lemon zest, a tablespoon of lemon juice, and most of the grated cheese. Toss until the cheese melts into the sauce.
Taste and adjust salt, pepper, and lemon juice.
Finish with freshness. Sprinkle in chopped parsley and toss once more. If you like extra kick, finish with a pinch more chili flakes or a drizzle of chili oil.
Serve immediately. Top each bowl with the remaining cheese. For texture, add toasted breadcrumbs on top.