Preheat a grill or cast-iron skillet over medium-high heat until very hot.
Season the flank steak evenly on both sides with smoked paprika, garlic powder, sea salt, and black pepper.
Grill the steak for 4 to 5 minutes per side for medium-rare, then transfer to a cutting board to rest for 5 minutes before slicing against the grain into thin strips.
Heat the toasted sesame oil in a large wok or non-stick skillet over medium heat.
Whisk the egg in a small bowl and pour into the skillet, scrambling quickly until just set, then remove the egg and set it aside.
Add the frozen peas, carrots, and the white parts of the sliced green onions to the skillet, sautéing for 3 to 4 minutes until tender.
Increase the heat to medium-high and add the cooked brown rice and tamari, stir-frying for 3 minutes until the rice is heated through and slightly crispy.
Fold the sliced steak, scrambled egg, and the remaining green onion tops into the rice mixture, tossing for 1 minute to combine everything before serving.