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1
Cut tips off 12 asparagus spears and reserve.
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2
Cut all spears into 1/2-inch pieces and cook in a saucepan of salted boiling water until tender, about 6 minutes.
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3
Transfer cooked asparagus with a slotted spoon to a blender and puree with 1 cup cooking liquid, reserving remaining cooking liquid in pan.
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4
Keep puree warm in a small saucepan.
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5
Have ready a bowl of ice and cold water.
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6
Return reserved cooking liquid to a boil and blanch reserved asparagus tips until just tender, about 3 minutes.
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7
Drain tips and immediately transfer to ice water to stop cooking.
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8
Drain tips and reserve for garnish.
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9
Scrub potato and cut lengthwise into four 1/2-inch-thick slices.
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10
In saucepan cook potato slices in salted boiling water to cover until tender, about 5 minutes, and transfer with a slotted spoon to a bowl.
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11
Keep potatoes warm, covered.
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12
Pat snapper dry and season with salt and pepper.
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13
In a large non-stick skillet heat oil over moderate heat until hot but not smoking and cook fish, skin sides down, about 3 minutes, or until skin is golden brown.
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14
Turn fish over and cook 2 minutes more, or until just cooked through.
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15
Whisk lemon juice and salt and pepper to taste into asparagus puree.
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16
Spoon some sauce onto 4 plates and top each portion with a potato slice and a fish fillet.
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17
Garnish fish with asparagus tips and serve remaining sauce on side.
