Boil water in a big pot, salt generously, and cook the pasta to al dente. Reserve a splash of the starchy water before you drain. You’ll thank yourself later.
Meanwhile, heat olive oil in a skillet over medium heat. Add minced garlic and sauté until fragrant, about 30 seconds to a minute—don’t burn it or you’ll be tasting it for days.
Pour in crushed tomatoes and broth. Stir, bring to a simmer, then reduce heat. Let it bubble gently for 5–7 minutes to marry the flavors.
Stir in Parmesan, red pepper flakes (if using), and a pinch of salt and pepper. If the sauce feels thick, loosen it with a bit of the reserved pasta water.
Add the drained pasta to the skillet and toss until coated. Finish with lemon juice, fresh herbs, and a final grate of cheese.