Place the ribeye in the freezer for 20 minutes to firm up the meat. When the meat is firm, slice the ribeye into thin strips against the grain (the muscle fibers).
Transfer the beef strips into a plastic bag or a bowl. Set aside.
Whisk the ingredients for the marinade together until combined. Pour the marinade over the beef. Stir the beef into the marinade until completely coated. Place the beef in the fridge for at least one hour or overnight for optimal flavor. Stirring the beef periodically or turning the bag over to make sure all the beef has time in the marinade.
Remove the beef from the fridge and remove it from the marinade. Transfer it to a plate and let excess moisture drip off the beef. Set the marinade aside. Let the beef rest at room temperature for 10-15 minutes.
Heat the avocado oil in a large cast iron skillet over high heat. When the cast iron is hot, add the beef to the pan. Sear the beef for 2-3 minutes on each side. Remove it from the pan. Add the sesame seeds, green onions, and cilantro to the beef and toss. Set aside.
Leave the beef drippings in the pan and add the bell peppers, white onion, and garlic to the pan. Season with salt and saute for 4-5 minutes until just cooked, not soggy. Remove from heat.
Add the excess marinade to a saucepan and bring to a boil. Let it simmer for 5 minutes. Set aside.
Evenly distribute the beef, rice, vegetables, and kimchi in bowls. Top the beef with the boiled extra marinade if desired. Serve with a fresh squeeze of lime juice.