In a small bowl, whisk together the soy sauce, dark brown sugar, sesame oil, and gochujang until well combined. Set this sauce aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the ground beef and cook until browned, breaking it up with a wooden spoon, about 5-7 minutes.
Add the chopped onion, minced garlic, and minced ginger to the skillet. Stir and cook for another 2-3 minutes until the onion is translucent.
Add the chopped red bell pepper, shredded carrots, and sliced mushrooms. Stir well and cook for about 5 minutes.
Pour the prepared sauce over the beef and vegetables. Stir to coat evenly and let it simmer for an additional 2-3 minutes.
Remove from heat and stir in the chopped scallions. Serve over steamed rice or cooked noodles, sprinkled with toasted sesame seeds.