Place the steak in the freezer for 30 minutes to make it easier to slice thinly. On a cutting board, very thinly slice the beef, trimming off any excess fat.
While the beef is in the freezer, in a bowl, combine the soy sauce, hoisin, gochujang and half of the sesame oil. Combine the beef slices with one-quarter of the sauce and refrigerate for 30 minutes. Set the remaining sauce aside for serving.
Meanwhile, in a bowl, combine the cucumbers, carrots, pear, rice vinegar, sesame seeds and remaining sesame oil. Add a generous pinch each of sugar and salt. Gently toss to combine. Set aside, stirring occasionally, until ready to serve.
In a Rice Pot, combine the washed rice with 2 ½ cups (625 ml) cold water. Season with salt. Bring to a boil. Cover with the lid and simmer over low heat for 12 to 15 minutes. Remove from the heat and let sit for 10 minutes, covered. Fluff the rice with a fork.
In a Skillet, heat 1 tbsp (15 ml) of the vegetable oil over medium-high heat. Add the beef, mushrooms and spinach. Cook, stirring, until the beef is just cooked through and the mushrooms are tender, about 5 minutes. Transfer to a bowl and keep warm. Wipe out the Skillet.
In the same Skillet, heat the remaining vegetable oil over medium-high heat. Carefully crack the eggs into the Skillet and cook just until the whites are set but the yolks are still runny. Season with gochugaru and salt.
Divide the rice among 4 Cereal Bowls. Top with the beef mixture, the marinated vegetables and fried eggs. Serve with the reserved sauce and toppings of your choice.