Boil the spaghetti: Bring a large pot of salted water to a boil and cook the spaghetti according to the package directions until al dente. Scoop out 1 cup of the pasta water, then drain.

Brown the mushrooms: While the pasta cooks, heat the olive oil and 1 tablespoon of the butter in a large skillet over medium-high heat. Add the mushrooms in an even layer and let them sit undisturbed for 3-4 minutes, then stir and cook another 3-4 minutes until deeply golden and any liquid has cooked off.

Add the garlic and seasoning: Push the mushrooms to the side and add the remaining 2 tablespoons butter to the pan. Stir in the garlic, salt, pepper, red pepper flakes if using, and thyme, and cook for about 1 minute until the garlic is fragrant but not browned.

Build the sauce: Pour in about 1/2 cup of the reserved pasta water and let it bubble for a minute, scraping up any browned bits from the bottom of the pan.

Toss the pasta: Add the drained spaghetti to the skillet along with the parmesan. Toss well, adding more pasta water a splash at a time, until the cheese melts into a glossy sauce that coats the noodles.

Finish and serve: Stir in the parsley and lemon juice, taste and adjust the salt, and serve right away with more parmesan on top.