Prepare the marinade by whisking soy sauce, brown sugar, 1 tablespoon sesame oil, ginger, and garlic in a medium bowl.
Add the sliced steak to the marinade and refrigerate for 30 minutes.
Rinse the jasmine rice and cook according to package instructions until tender.
Prepare the dressing by whisking gochujang, rice vinegar, 1 tablespoon soy sauce, honey, and 1 teaspoon sesame oil in a small bowl.
Sauté the baby spinach in a lightly oiled pan until wilted; remove and set aside.
Heat a heavy skillet or wok over high heat and sear the marinated steak in small batches until caramelized, approximately 3-5 minutes per batch.
Divide the cooked rice into four serving bowls.
Top each bowl with equal portions of seared steak, shredded carrots, sliced cucumber, sautéed spinach, and kimchi.
Drizzle each bowl with the spicy sesame dressing and garnish with toasted sesame seeds.