For the french fries: Heat the oil in a heavy skillet over medium heat. Add the potatoes and saute for about 15 minutes. Drain on paper towels.
For the beef and vegetables: Heat 1/2 cup of the oil over high heat in a skillet. Add the beef and saute until browned on all sides. Move the beef to a plate and set aside, covered.
Return the pan to medium-high heat and add the remaining 1 1/2 tablespoons oil. Add the onion pieces and saute until the edges are slightly softened, about 2 minutes. Add the parsley, soy sauce, balsamic vinegar, lime juice, chile peppers, tomatoes and some salt and pepper and saute until the tomatoes have softened, 2 minutes. Add the beef and purple potatoes and toss.
Serve the beef and french fries alongside rice and sprinkle with chopped parsley.