Preheat the oven to 400°F. Line a baking sheet with parchment paper. Place the salmon fillet on the sheet and drizzle with soy sauce, sesame oil, minced garlic, and ginger. Season with salt and pepper. Bake for 12-15 minutes or until the salmon is cooked through and flakes easily with a fork.
While the salmon is baking, prepare the vegetables. In a skillet over medium heat, lightly sauté the spinach, carrots, and bean sprouts separately for about 2-3 minutes each, just until tender. Season with salt and pepper to taste.
In a separate pan, fry the eggs sunny-side up or to your desired doneness.
To assemble the bibimbap, divide the cooked jasmine rice among four bowls. Arrange the sautéed spinach, carrots, cucumber, and bean sprouts on top of the rice. Flake the baked salmon and place it in the center of each bowl.
Top each bowl with a fried egg and a dollop of gochujang. Sprinkle with sesame seeds.
Serve immediately, allowing everyone to mix their bibimbap together before eating.