Rinse the short-grain rice in cold water until the water runs clear, then cook using a 1:1.25 rice-to-water ratio in a rice cooker or covered pot.

In a large bowl, whisk together soy sauce, sesame oil, brown sugar, garlic, and ginger to create the marinade.

Add the sliced steak to the marinade, tossing to coat thoroughly; allow to marinate at room temperature for 15 minutes.

In a small ramekin, combine mayonnaise, gochujang, and lime juice, whisking until a smooth, uniform sauce is formed.

Set a heavy cast-iron skillet over high heat. Once smoking slightly, add the steak in a single layer (working in batches) and sear for 2-3 minutes until caramelized.

Distribute the cooked rice into four bowls, then top each with a portion of the seared steak, carrots, and kimchi.

Drizzle the spicy cream sauce over each bowl and garnish with sliced scallions and toasted sesame seeds.