Cook the rice according to package instructions until soft and fluffy. Keep warm.
Slice the steak into thin strips against the grain. Season with salt and black pepper.
Heat olive oil in a pan over medium-high heat. Add steak in a single layer and cook until browned on both sides. Remove if needed and cook in batches.
Reduce heat slightly. Add butter and minced garlic to the pan. Stir gently until fragrant.
Pour in soy sauce and brown sugar. Mix well and let the sauce simmer until slightly thickened. Return steak to the pan if removed earlier and coat evenly.
Add broccoli to the pan and cook until just tender. Add a splash of water if needed to help steam.
Divide warm rice into bowls. Top with steak, broccoli, and shredded carrots.
Spoon extra sauce over the top. Garnish with green onions and chili flakes if desired. Serve immediately.