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1
Break the woody ends from the asparagus and peel the stalks if necessary.
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2
(If you use thin asparagus, you wont have to peel them at all; thicker asparagus should be peeled from the bottom of the flower to the end of the stalk.)
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3
Break or cut off the flower ends and cut the stems into 1/2-inch sections (it looks a little nicer if you cut the stems on a diagonal, but this is hardly essential).
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4
Put half the butter or oil in a deep 10- or 12-inch skillet or a broad saucepan and turn the heat to medium-high; when it melts, add the onion and cook, stirring occasionally, until softened and beginning to brown, 3 to 5 minutes.
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5
Add the pasta and cook, stirring occasionally, until it begins to brown, about 5 minutes more.
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6
Add a ladleful of stock.
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7
As the stock is absorbed and the pasta swells, add more stock and continue to stir once in a while, until the pasta is beginning to get tender, about 5 minutes.
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8
Add the asparagus stalks and continue to add stock as needed until the pasta is just about done, another 5 minutes or so.
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9
Add the asparagus tips and a little more stock, stirring until the tips are crisp-tender, the pasta is cooked to your liking, and the mixture is moist but not soupy (add a little more stock if necessary).
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10
Stir in the remaining butter or oil and the Parmigiano-Reggiano to taste if you like and serve.
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11
Substitute carrots, cut into small chunks, for the asparagus; they add vivid color and a marked sweetness.
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12
Or experiment with other vegetables.
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13
Any sharp grated cheese will fill in well for the Parmigiano-Reggiano, especially pecorino Romano.
