Bring a large pot of water to a rolling boil and add a large pinch of salt.
Add the angel hair pasta and cook according to package instructions, about 4–5 minutes, until al dente.
While the pasta cooks, heat a large frying pan over medium-high heat and add the olive oil.
Add the sliced garlic to the pan and cook 1–2 minutes, stirring, until fragrant and not browned.
Stir in the chopped dried chili (or 1/4 tsp chili flakes) and dried oregano and cook briefly to combine.
Reserve 3 tablespoons of the pasta cooking water in a small bowl or mug, then drain the pasta using a fine-mesh sieve or colander.
Add the drained pasta to the frying pan with 1 tablespoon of the reserved cooking water and toss to coat in the oil.
Add additional reserved cooking water as needed to create a thick, glossy sauce that coats the pasta.
Season with sea salt and freshly ground black pepper to taste, then stir in the chopped parsley.
Divide the pasta among plates and garnish with grated Parmesan cheese, if desired.
