To make the tomato chutney: In a medium bowl, toss together tomatoes, onions, cilantro, mint, vinegar, ginger, chiles, and salt. Cover and refrigerate until ready to serve.
Separate the pieces of cold rice with your hands until loose.
In a large wok or pan, drizzle 2 tablespoons of the oil over high heat. Once heated, Pour in the eggs and swirl to coat the bottom of the wok. Once the bottom has set, gently lift the edges to allow to raw egg on top to pour underneath. Once set, transfer with a large slotted spoon to a plate.
Stir the shallots, beans, carrots, and garlic in the pan until the garlic is fragrant and the shallots are softened, 1-2 minutes. Stir in the chicken and cook until golden. Reduce heat to medium high and drizzle in the remaining 1 tablespoon oil. Toss in the separated rice and cook until heated through.Add the soy sauce, salt, and pepper, tossing to combine. Add the fried egg on top and break apart as it is mixed into the rice.
Sprinkle with green onions and serve immediately with tomato chutney.