Prepare a large bowl of ice water. Snap off and discard woody bases from asparagus. In a covered Dutch oven cook asparagus in a small amount of boiling water for 4 to 6 minutes or just until crisp-tender; drain. Immediately plunge asparagus into the ice water; cool. Remove asparagus; pat dry with paper towels. Set aside.
For sauce, in a large skillet heat oil over medium-high heat. Add onion, garlic, salt, and pepper; cook until onion is tender, stirring occasionally. Stir in broth, sherry, and cream cheese. Bring to boiling. Add mushrooms; cook for 3 to 4 minutes or until mushrooms are tender and mixture is slightly thickened, stirring occasionally. Stir in Parmesan cheese. Serve asparagus with sauce. Sprinkle with thyme.