1. In a blender or food processor, combine egg yolks, garlic, lemon zest, and lemon juice; pulse until smooth. Combine grapeseed and olive oils in a liquid measuring cup. With blender running, slowly drizzle in oils in a thin stream until mixture is thick, 2 minutes. Add salt, pepper, and parsley; pulse to blend.
2. Snap tough ends from asparagus. Lay each stalk flat on a cutting board and, using a vegetable peeler, peel to about 1 inch below the tip.
3. Bring at least 1 in. water to a simmer in a large frying pan or wide pot. Lay asparagus in pan and simmer, covered, until tender, 3 to 5 minutes (white asparagus may take longer). Cool in a bowl of ice and water; drain.
4. Serve asparagus on a large platter with aioli spooned across, or on the side.
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