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In a large pot of boiling salted water, cook the asparagus until bright green and tender, about 3 minutes; transfer to a colander and refresh under cold water. Drain and pat dry.
Roast the peppers directly over a gas flame or under the broiler, turning, until charred all over. Transfer to a medium bowl, cover with plastic wrap and let steam for 10 minutes. Peel the peppers and cut them into 1/4-inch-thick strips.
In a medium bowl, stir together the vinegar, capers, mustard, tarragon, garlic and onion; season with salt and pepper. Whisk in the olive oil.
Arrange the asparagus on a serving platter. Lay the roasted pepper strips over the asparagus and drizzle with half of the vinaigrette. Crumble the goat cheese on top. Garnish with the chopped olives and the Parmigiano shavings and serve, passing the remaining vinaigrette at the table.
The recipe can be prepared through Step 3 up to 8 hours ahead. Refrigerate the asparagus, peppers and vinaigrette separately.