Snap off and discard woody bases from fresh asparagus. Cut into 2 inch pieces. Set aside.
In a 2 quart saucepan, cook potatoes, covered, in a small amount of boiling water for 10 minutes. Add asparagus. Cook, covered, about 8 minutes more or until asparagus is crisp-tender and potatoes are tender. Drain. Transfer vegetables to a serving bowl.
Meanwhile, for dressing, combine the olive oil, shredded lemon peel, salt and thyme, and a squeeze of fresh lemon. Add to vegetables, toss to gently coat. If desired, garnish with a lemon peel curl and fresh thyme.