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1
Hold a sharp knife at a 45-degree angle and cut the florets from the broccoli stems into a bowl.
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2
Chop remaining stems into small pieces and transfer stems to a separate bowl.
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3
Heat 2 tablespoons olive oil with butter in a skillet over medium heat and cook garlic in the hot oil-butter mixture, stirring often, until garlic is soft but not browned.
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4
Sprinkle in 1 teaspoon red pepper flakes and salt.
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5
Pour chicken stock into skillet and bring to a simmer.
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6
Stir broccoli stems into the stock mixture and simmer until tender, 10 to 12 minutes.
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7
Add a little water or stock if mixture starts to dry out.
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8
Stir broccoli florets into skillet and cook broccoli sauce until florets are bright green and slightly tender, 3 to 4 minutes.
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9
Bring a large pot of salted water to a boil and stir in angel hair pasta.
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10
Cook, stirring occasionally, until pasta strands are almost tender, about 4 minutes.
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11
Drain and transfer to a large pot.
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12
Pour broccoli sauce over pasta, stir with a wooden spoon, and mix in 1/2 cup Parmigiano-Reggiano cheese.
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13
Cover pot with a lid and let stand until pasta absorbs excess liquid and finishes cooking, about 2 minutes.
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14
Serve in bowls and sprinkle each serving with a dusting of Parmigiano-Reggiano cheese and a pinch of red pepper flakes.