In a large skillet, heat oil over medium. Add onion, carrots, and celery and cook, stirring frequently, until vegetables are softened, 10 minutes. Transfer mixture to a 5-to-6-quart slow cooker and add beef, tomatoes, broth, garlic, 1 teaspoon salt, and 1/4 teaspoon pepper.
Cover and cook on high, 6 hours, stirring occasionally. To serve, divide brown rice and stew among six bowls and top with yogurt and parsley.
To store, refrigerate stew in an airtight container, up to 3 days, or freeze, up to 3 months.
Eat Smart: Use Greek yogurt in place of sour cream to garnish chilis and stews to get creamy tang without the fat. Ask your butcher to trim away most of the fat from the beef chuck; it will still become tender and flavorful in a slow cooker. Use bulgur in place of brown rice, if you like.