Sauté the beef: Preheat a skillet over medium-high heat. Add the sesame oil and sauté the beef until golden brown. Remove from the skillet and set aside.
Cook the noodles: In a pot of salted boiling water, cook the lo mein noodles according to the package instructions. Drain well.
Cook the vegetables: In the same skillet, add olive oil and sauté the onions until golden brown. Add the carrots and cook until softened. Add the broccoli and sauté for about 3 minutes.
Add garlic: Add the minced garlic and ginger, sauté for 1 more minute.
Combine and simmer: Add the cooked beef back into the skillet. Stir in the beef broth, brown sugar, and soy sauce. Bring to a simmer until the broccoli is tender.
Add noodles: Stir in the cooked noodles until everything is well combined.
Prepare the Eggs: In a bowl, whisk together eggs, salt, and rice wine vinegar until foamy and pale yellow.
Heat a wok or pan over medium heat and coat with a small amount of oil. Stir-fry garlic for 30 seconds. Add tomatoes and granulated sugar. Reduce heat to medium and stir for 3 minutes until soft and juicy. Add a splash of water if needed. Pour in the egg mixture and scallions, cook for 50 seconds until mostly set but still slightly runny. Turn off heat, scramble gently with chopsticks until firm.
Serve: Plate the lo mein with tomato egg stir fry. Serve alongside chilled coconut water and fortune cookies. Enjoy!