Step 1: Cook the noodles and broccoli - Fill a large pot with water and bring it to a boil. Add the lo mein noodles and cook according to the package directions. About halfway through cooking the noodles, add the broccoli florets to the pot. Once everything is tender, drain well and set aside.
Step 2: Cook the beef and vegetables - Heat the oil in a large skillet over medium high heat. Add the shredded carrots and thinly sliced steak. Cook for five to eight minutes, stirring often, until the steak is cooked to your liking and the carrots are softened.
Step 3: Make the sauce - In a small bowl, combine the minced garlic, hoisin sauce, soy sauce, brown sugar, ground ginger, pepper, and red pepper flakes. Stir until everything is well mixed.
Step 4: Bring it all together - Add the cooked noodles and broccoli to the skillet with the beef. Pour the sauce over everything and gently toss until the noodles are fully coated and heated through.
Step 5: Finish and serve - Remove from heat and top with chopped green onions or sesame seeds if desired. Serve warm and enjoy.