Combine potatoes, roast beef, onion, bell pepper, thyme and ground pepper in bowl; toss to blend well.
Heat oil in heavy medium skillet over medium heat.
Add potato mixture; press to flatten with spatula. Cover and cook until bottom begins to crisp, about 5 minutes.
Using metal spatula, turn over browned bottom in sections. Cook uncovered until hash is thoroughly flecked with brown bits and onion and bell pepper are tender, turning over browned bottom in sections 2 more times, about 10 minutes longer. Divide between plates and serve.