Heat a skillet over medium-high heat and brown the ground beef until fully cooked. Drain any excess grease.
Transfer the cooked beef to the slow cooker.
Add the matchstick carrots, sliced red bell pepper, and chopped scallions to the slow cooker.
In a small mixing bowl, whisk together the minced garlic, low sodium soy sauce, brown sugar, and chicken stock until smooth.
Pour the sauce mixture over the beef and vegetables in the slow cooker and stir to combine.
Cover and cook on Low heat for 4 to 6 hours (or High heat for 2 to 3 hours).
Approximately 30 minutes before serving, break the dry ramen noodles into chunks and add them to the slow cooker. Discard the seasoning packets.
Stir the noodles well to ensure they are submerged in the liquid. Cover and continue cooking for 20-30 minutes, or until the noodles are tender.
Garnish with sesame seeds and extra green onions before serving warm.