Fill a very large pot halfway with water. Add plenty of salt, cover, and bring to a boil.
When the water boils, cook the spaghetti one minute less than it says on the package. Toward the end of cooking, scoop out and reserve ½ cup of the cooking water.
Meanwhile, set a large frying pan over medium-low heat. Add the olive oil and butter and warm until butter is melted.
A?dd the garlic, salt, and chili flakes.
Cook, stirring from time to time, until garlic is very fragrant, just a few minutes. Reduce heat if necessary to prevent browning.
Drain pasta (reserving ½ cup of the cooking water).
I?nto the frying pan, whisk the lemon juice, grated cheese, pepper, and reserved cooking water. Bring to a simmer.
A?dd drained pasta to pan and toss for a minute or two to coat well, letting the silky sauce thicken enough to coat the strands.
O?ff the heat, stir in the parsley.