Combine 2 tablespoons of gochujang, 2 tablespoons sesame oil, and 1 tablespoon of honey with the soy sauce and mirin in a small bowl and whisk to combine to create the marinade for the beef.
Coat the beef in a shallow dish with the marinade and let it marinade at room temperature for 30 minutes.
Mix 2 tablespoons of gochujang, 1 tablespoon of sesame oil, and 1 tablespoon of honey to create the sauce for the Bibimbap.
Once the beef has finished marinading, place the beef along with the marinade in a skillet heated to medium-high heat and sauté until the beef is cooked and the marinade has reduced, approximately 3 to 4 minutes. Set aside.
Cook the jasmine rice per the package instructions, approximately 20 minutes.
While the rice is cooking, add a tablespoon of vegetable oil and the carrots to a skillet heated to medium high heat and cook for 1 to 2 minutes or until they begin to soften. Remove and set aside.
Add another tablespoon of vegetable oil and the mushrooms and cook for 1 to 2 minutes. Remove and set aside.
Add another tablespoon of vegetable oil and the bean sprouts to the skillet and cook for 1 to 2 minutes. Remove and set aside.
Add the last tablespoon of vegetable oil and the spinach and cook until the spinach is fully wilted, approximately 2 to 3 minutes. Remove and set aside.
Add the butter to the skillet and, once melted, add the eggs and cook sunny-side up ensuring that the yolk is still runny but the whites are fully cooked.
Place a scoop of the rice in the center of a plate and surround it with the beef and vegetables. Gently place the egg on top and sprinkle with the sesame seeds and seaweed, if using it.