In a large skillet heat the oil over high heat until it is smoking. Add the broccoli, give it a quick stir and cook it covered, stirring occasionally, for 3 minutes. (It should look crispy and brown around the edges.) Turn the heat to low and cook it for 2 minutes more or until it is just tender. Add the red pepper flakes, garlic and salt and pepper to taste and cook the mixture for 1 minute. While the broccoli mixture is cooking, boil the angel hair pasta in a large pot of salted water for 3 to 5 minutes or until it is just al dente and drain it. Add the cooked pasta, chicken stock and half of the parmesan cheese to the skillet and bring the mixture to a simmer. Divide among 4 bowls. Top each portion with the remaining cheese.
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