Slice the flank steak against the grain into very thin strips and place them in a medium glass bowl.
In a small jar, whisk together the coconut aminos, toasted sesame oil, grated Asian pear, minced ginger, garlic, and black pepper.
Pour the marinade over the beef strips, tossing well to coat, and let it sit at room temperature for 20 minutes.
Heat a large cast-iron skillet over high heat until it is smoking slightly.
Add the marinated beef to the hot skillet in a single layer, searing for 1-2 minutes per side until deeply browned and caramelized.
Toss in the shredded carrots for the last 30 seconds of cooking just to soften them slightly.
Serve the bulgogi beef and carrots over the cooked brown rice.
Garnish with sliced green onions and a sprinkle of sesame seeds before serving.