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1
In a small saucepan simmer reserved asparagus ends in water, covered, 15 min.
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2
Remove and throw away asparagus ends with slotted spoon and bring water to a boil.
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3
Add in reserved asparagus tips and cook, uncovered, over high heat till crisp-tender, about 3 min.
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4
Transfer asparagus tips with slotted spoon to a colander, reserving cooking liquid, and rinse under cool water to stop cooking.
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5
Drain tips well.
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6
In a 4-qt heavy saucepan cook onions in butter with salt and pepper to taste over moderate heat, stirring till pale golden brown.
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7
Add in asparagus stalk pcs, broth, and reserved cooking liquid and simmer, covered, 15 min, or possibly till asparagus pcs are tender.
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8
Basil cream:Make basil cream while soup simmers: In a small saucepan bring cream to a boil and stir in basil and salt.
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9
Cook mix over high heat, stirring, till basil is wilted, about 5 - 10 seconds, and in a blender puree mix.
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10
Return basil cream to small saucepan and keep hot.
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11
Puree soup in cleaned blender in small batches and return to 4-qt saucepan, thinning with water if you like.
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12
Season soup with salt and pepper and heat over moderately low heat, stirring occasionally, till heated through.
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13
Divide soup among 6 bowls and add in asparagus tips, arranging them decoratively.
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14
Drizzle basil cream over each serving.
