Combine finely ground porcini mushrooms, egg yolk, 3 tablespoons hot water, sherry, ½ teaspoon salt, and mustard in a food processor. With processor running, gradually drizzle in oil, and process until mixture is creamy, about 45 seconds, stopping to scrape down sides as needed. Transfer to a small bowl, and season with salt to taste. Set mushroom aioli aside at room temperature until ready to use.

Bring rice vinegar, sugar, 1 teaspoon salt, and remaining ¼ cup hot water to a simmer in a small skillet over medium-high, stirring occasionally to dissolve sugar. Remove from heat, and stir in asparagus. Let stand until asparagus is slightly softened, 5 to 8 minutes. Drain asparagus, and pat dry with paper towels.

Gently toss together crabmeat, sour cream, lemon juice, and remaining ½ teaspoon salt in a medium bowl. Fold in pickled asparagus, reserving about ¼ cup asparagus for garnish.

Spread mushroom aioli evenly over each toast slice (about 2 ½ tablespoons each). Top evenly with crab mixture (about ⅓ cup each). Garnish with reserved ¼ cup pickled asparagus, lemon zest, and chives. Serve immediately.