Place steak, 1⁄4 cup soy sauce, garlic and 2 tablespoons lime juice in a large bowl. Leave 10 minutes.
Preheat grill to high heat; cook steak 2 minutes each side. Set aside.
Place broccoli in a steamer basket. Fill a large pan with boiling water to a depth equal to the width of two fingers; bring to a boil. Reduce heat to a simmer. Place steamer basket on top of pan. Cover, cook broccoli 5 to 6 minutes or until crisp–tender. Leave to cool 10 minutes. Place in a large bowl with mint, basil and coriander. Add cucumber slices.
Slice steak and add to salad. Combine chillies, sugar, remaining 1⁄4 cup soy sauce and remaining 3 tablespoons lime juice in a bowl. Stir gently into salad. Pile salad onto serving plates.