Stir the picante sauce, orange juice, oil, brown sugar, soy sauce, mustard and ginger in a shallow, nonmetallic dish or gallon size resealable plastic bag. Add the beef and turn to coat. Cover the dish or seal the bag and refrigerate for 1 hour or overnight.
Lightly oil the grill rack and heat the grill to medium. Grill the beef for 10 minutes for medium-rare or to desired doneness, turning the beef over once during grilling and basting often with the picante sauce mixture.
Heat the remaining picante sauce mixture in a 1-quart saucepan over medium-high heat to a boil. Reduce the heat to low. Cook for 10 minutes or until the mixture is thickened, stirring occasionally.
Slice the beef and serve with the picante sauce mixture and rice. Sprinkle with the parsley.
For a flavor twist, substitute 1 can (about 20 ounces) crushed pineapple, undrained, for the orange juice.