Prepare the brown rice according to package instructions and set aside.
In a small bowl, whisk together the tamari, honey, minced ginger, minced garlic, and red pepper flakes to create the marinade.
Thinly slice the flank steak against the grain and toss with the marinade and black pepper; let sit for 10 minutes to absorb the flavors.
Bring a small pot of water to a boil, carefully lower in the egg, and simmer for 6.5 minutes for a jammy yolk, then immediately transfer to an ice bath.
Steam the broccoli florets until they are tender-crisp and bright green.
Heat the sesame oil in a large skillet over medium-high heat until shimmering.
Add the beef to the skillet in a single layer and sear until caramelized and cooked through, about 2-3 minutes per side.
Assemble the bowl by placing the rice at the bottom, topped with the seared beef, steamed broccoli, shredded carrots, and the peeled, halved egg.
Garnish with thinly sliced green onions before serving.