1. Bring 3 quarts water to a boil in a large saucepan. Peel bottom 2 inches of white and green asparagus. Cook white asparagus in boiling water 5 minutes or until crisp-tender; remove with a slotted spoon to a colander. Rinse under cold water; drain well. Cook green asparagus in boiling water 2 minutes or until crisp-tender; remove with a slotted spoon to a colander. Rinse under cold water; drain well. Cut asparagus diagonally into 1 1/2-inch pieces.
2. Melt butter in a large nonstick skillet over medium-high heat; swirl to coat. Add shallot; sauté 1 minute, stirring constantly. Add morels and 1/4 teaspoon salt; sauté 5 minutes or until mushrooms are lightly browned. Add asparagus, remaining 1/4 teaspoon salt, oil, and pepper; toss gently to coat. Cook 2 minutes or until asparagus is thoroughly heated.