A creamy mustard-and-lemon dressing emulsified with a soft-boiled egg yolk takes this asparagus salad over the top.
Dressing: Place egg in a small saucepan; cover with water by 1 inch. Bring to a boil, then remove from heat. Cover pot and let stand 8 minutes. Run egg under cold water to stop cooking. Peel egg; remove white and reserve for another use. Press yolk through a fine sieve into a small bowl.
Meanwhile, remove peel and pith from 1 lemon. Holding fruit over another bowl, cut between membranes, allowing segments to drop in. Squeeze juice from membranes into bowl; discard membranes. Coarsely chop segments (you should have 2 tablespoons). If you don't have 2 tablespoons of juice or segments, use second lemon.
Add mustard, lemon juice, sugar, and salt to bowl with yolk. Gradually add oil, whisking constantly until creamy and emulsified. Stir in lemon segments; season with salt and pepper. Dressing can be refrigerated up to 1 week; return to room temperature before using.
Salad: Preheat oven to 350 degrees. Spread almonds in a single layer on a rimmed baking sheet and toast until golden brown and fragrant, 10 to 15 minutes. Let cool completely.
Bring a large pot of salted water to a boil. Add asparagus; return to a boil and cook, uncovered, until bright green and tender, 2 to 3 minutes. Drain. Run under cold water to stop cooking; drain again and pat dry.
Remove lemon zest in long strips with a vegetable peeler. Slice zest very thinly into strips; you should have about 2 tablespoons (or use a channel zester). Remove remaining peel and pith from lemon; holding fruit over a bowl, cut between membranes, allowing segments to drop in.
Arrange asparagus on a platter with cheese. Sprinkle with almonds, zest, lemon segments, and basil. Drizzle with 1/4 cup dressing (reserve remainder for another use). Season with salt and pepper and serve, garnished with whole basil leaves.