In a bowl, toss the beef with cornstarch until evenly coated.
In a separate bowl, whisk together the soy sauce, brown sugar, water, hoisin sauce, ginger, garlic, and red pepper flakes (if using).
Heat vegetable oil in a large skillet or wok over high heat. Add the beef and cook, stirring constantly, until browned and cooked through, about 2-3 minutes. Remove the beef from the skillet and set aside.
Pour the sauce into the skillet and bring to a simmer. Cook for 2-3 minutes, or until the sauce has thickened slightly.
Add the beef back to the skillet and toss to coat. Cook for another minute to heat through.
Cook the ramen noodles according to package directions. Drain and divide among bowls.
Top the ramen noodles with the Mongolian beef and sauce. Garnish with sesame seeds and sliced green onions, if desired.