Heat a skillet over medium-high heat. Add sesame oil and sauté the beef until golden brown. Remove from the skillet and set aside.
Bring a pot of salted water to a boil. Cook the lo mein noodles according to package directions, then drain and set aside.
In the same skillet, heat olive oil. Sauté onions until golden brown, then add carrots and cook until softened. Add broccoli and cook for about 3 minutes. Stir in garlic and sauté for 1 more minute.
Return the cooked beef to the skillet. Stir in beef broth, brown sugar, and soy sauce. Simmer until the broccoli is tender, then add the noodles and toss to combine.
Prepare the tomato egg stir fry: In a bowl, beat eggs with salt and rice wine vinegar until foamy.
Heat a wok over medium-high until very hot. Coat the bottom with a little oil. Pour in the egg mixture and cook for about 50 seconds until mostly set but still slightly runny. Turn off the heat and quickly scramble the eggs with chopsticks for a few seconds, then transfer to a bowl.
Add a little more oil to the wok and reheat over high. Stir-fry the minced garlic for 30 seconds, then add tomatoes and reduce heat to medium. Cook for about 3 minutes until tomatoes are soft and release juice. If the pan is too dry, add a splash of water. Stir in salt and granulated sugar.
Return the eggs to the pan and stir to combine with the tomatoes. Keep stirring for about 50 seconds, gradually adding soy sauce. Stir in most of the scallion, reserving some for garnish.
Plate the lo mein with the tomato egg stir fry on the side. Sprinkle the remaining scallion over the top.
Serve with fortune cookies and a glass of cold coconut water.