Snap off tough ends of asparagus. Remove scales from stalks with a knife or vegetable peeler, if desired. Cut spears into 1-inch pieces. Set aside.
Cook potato in a Dutch oven in boiling water to cover 10 minutes. Add asparagus; cook 5 minutes or until potato is tender and asparagus is crisp-tender. Drain and set aside.
Coat Dutch oven with cooking spray; place over medium-high heat until hot. Add onion, garlic, and chile; saute until crisp-tender. Add cumin and oregano; saute 1 minute. Stir in tomato, broth, and vinegar. Bring to a boil; reduce heat, and simmer, uncovered, 5 minutes. Add potato mixture; toss lightly to coat. Sprinkle with cheese and cilantro. Serve warm.