In a medium saucepan, mix all soy sauce, beef broth, garlic, ginger, brown sugar, and red pepper flakes.
Add frozen meatballs and cook as directed on the package, usually about 20 minutes. (I like to use a pan big enough for the meatballs to be in a single layer, but small enough they are still touching on the sides.)
Once the meatballs are fully cooked and heated through, mix the cornstarch with water and stir into the sauce. Simmer 2 more minutes.
Boil water and cook Ramen noodles with the carrots for 2 minutes; drain and discard cooking water.
Add the cooked noodles and carrots to the meatballs/sauce. Toss until all the noodles and vegetables are coated in sauce.
Sprinkle with the green onions and more red pepper flakes.