Whisk together the gochujang, palm sugar, 2 teaspoons of the rice vinegar, and the sesame oil in a medium bowl and set aside.
Pulse the chuck and sirloin in a food processor until it resembles a coarse, medium grind, 8 one-second pulses. Add the gochujang mixture and pulse 2 more times to combine. Transfer to a medium bowl, cover, and refrigerate for 30 minutes.
Stir 1/2 cup of the kimchi together with the remaining 1 tablespoon vinegar, along with all of the ketchup and fish sauce and set aside.
Whisk the eggs with the soy sauce until homogenous.
Heat an 11-inch sauté pan or 15-inch wok over high heat for 5 minutes, then add 2 tablespoons of the peanut oil, followed by the mushrooms and 1 teaspoon of the salt. Sear, undisturbed, for 90 seconds, then stir and continue cooking until the mushrooms develop well-browned, crispy edges, about 2 minutes. Remove the mushrooms from the pan and drain on a paper towel-lined plate.
Add 1 tablespoon more peanut oil to the pan, followed by the ginger, garlic and remaining teaspoon of salt. Count to three, and then add all of the meat and any marinade remaining in the bowl. Cook, stirring constantly, until the meat is no longer pink, about 5 minutes. When the pan is almost dry, add the reserved kimchi-vinegar mixture and stir, scraping up any browned bits stuck to the bottom of the pan.
Add the spinach to the pan and cook, stirring, for 1 minute. Add the eggs and reserved mushrooms and continue to cook, stirring constantly, until scrambled and set, 30 seconds to 1 minute. Fold in the scallions and immediately transfer to a large serving bowl. Set aside while you fry the rice.
Heat the remaining 2 tablespoons of the peanut oil in the now-empty sauté pan over high heat just until it shimmers. Add the rice to the pan, mashing it into a thin layer, and cook undisturbed until you hear it start to crackle, about 5 minutes. Stir in the remaining 1/2 cup of kimchi and cook until just heated through, about 1 minute. Portion into 4 bowls; top with the meat, egg, and vegetable mixture; and garnish with sesame seeds. Serve.