Preheat oven to 475°F Arrange asparagus on rimmed baking sheet. Drizzle oil over and turn to coat. Sprinkle generously with salt and pepper. Roast until just tender, about 10 minutes.
Meanwhile, melt butter in large skillet over medium-high heat. Add shallot; sauté 1 minute. Add mushrooms; sauté until beginning to brown, about 5 minutes. Cover; cook until mushrooms are tender, about 3 minutes. Add wine; cook uncovered until wine is absorbed, about 2 minutes. Stir in parsley and tarragon. Season to taste with salt and pepper. (this can be done ahead of time and warmed up just before serving).
Divide asparagus among 4 plates. Top each serving with mushrooms.