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In a large saucepan bring at least 5 cups salted water to a boil and add the asparagus.
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Cook 4 minutes.
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Drain, reserving 3+1/2 cups cooking liquid.
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Place asparagus in a bowl of ice water to stop the cooking process.
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Drain and cut the tips off the asparagus.
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Cut the stalks into 1/4 inch rounds.
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Keep tips and stalks separate.
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Place chicken broth and reserved cooking liquid in a saucepan and bring to a simmer.
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Reduce heat to low.
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In a large saucepan, heat oil over medium heat.
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Add onion and saute 5 minutes.
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Add rice and continue sauteing 2 minutes, stirring.
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Add 3/4 c hot liquid and simmer, stirring frequently, until is absorbed.
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Add asparagus rounds and 3/4 cup hot liquid.
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Simmer, stirring frequently, until liquid is absorbed.
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Continue adding hot liquid, 3/4 cup at a time, simmering and stirring frequently, until rice is cooked and liquid has been absorbed.
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Mix in the reserved asparagus tips, butter and grated cheese.
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Season to taste with salt and pepper.
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Place into serving bowls and top with shaved Parmesan.