Put dried mushrooms in a heatproof bowl and pour boiling water over them. Let stand 20 minutes. Pour mushrooms with liquid through a paper towel-lined sieve into a small saucepan. Transfer mushrooms to a cutting board and finely chop. Add vinegar, shallots, sugar, 1/2 teaspoon salt, and half of mushrooms to saucepan and boil mixture until it is reduced to 2/3 cup, about 10 minutes. Whisk in 1/4 cup olive oil and add salt and pepper to taste. Sauce can be served warm or at room temperature. Preheat oven to 400°F with rack in upper third. Stir together remaining chopped mushrooms with softened goat cheese in a small bowl. Place a steamer basket in a 5-quart pot filled with 2 inches of water. Steam asparagus, covered, just until tender, 4 to 5 minutes. Transfer asparagus to a bowl of ice water to stop cooking, then drain and pat dry. Halve asparagus crosswise. Arrange bread slices on a large baking sheet. Brush with some olive oil and bake until golden, 10 to 12 minutes. Spread goat cheese mixture generously on toasts. To serve, place a toast in the center of a salad plate and arrange 4 or 5 stem ends of asparagus on each. Top stems with asparagus tips, arranging them perpendicular to stems. Drizzle asparagus and surrounding plate with vinaigrette.