Combine soy sauce, brown sugar, gochujang (if using), sesame oil, garlic, and ginger. Place steak in the marinade for 10–20 minutes at room temperature or up to 2 hours in the fridge. Reserve half the marinade for the pan sauce.
Cook rice according to package directions. For quick pickles, whisk 1/2 cup rice vinegar, 1 tablespoon sugar, and 1/2 teaspoon salt; pour over carrot and cucumber slices and let sit 10–15 minutes.
Heat a heavy skillet over medium-high heat with oil. Remove steak from marinade and sear 2–3 minutes per side for medium-rare. Transfer to a cutting board and rest 5–7 minutes.
Add reserved marinade to the hot pan and simmer 2–3 minutes until slightly thickened and glossy. Optionally whisk in a small knob of butter or a cornstarch slurry to thicken.
Slice steak thinly against the grain. Divide rice among bowls, top with sliced steak, drizzle pan sauce, add pickled vegetables and kimchi, and garnish with green onions and sesame seeds. Serve with lime wedges if desired.
Notes
Slice steak against the grain for maximum tenderness.
Make sure not to overcrowd the pan when searing to get a good crust.
Store components separately in the fridge for up to 3 days for best texture.