Place the shaved beef in a large bowl or zip-lock bag.
In a small bowl, whisk together all of the marinade ingredients. Pour the marinade over the shaved beef and toss until it's evenly coated. Refrigerate for at least 30 minutes, or up to 12 hours for the best flavor.
While the beef marinates, prepare the toppings by chopping the cucumber and green onions, cooking the rice, and stirring together the sriracha and mayo in a small bowl. Refrigerate the sauce until you're ready to assemble the bowls.
Heat a large skillet over medium-high heat. Working in batches if needed to avoid overcrowding the pan, add the marinated shaved beef and cook for 2-4 minutes, stirring frequently, until the beef is browned and lightly caramelized.
While the beef cooks, fry the eggs. Heat a small skillet over medium-high heat and lightly coat it with avocado oil. Crack in the eggs and cook to your preferred doneness. For sunny-side-up eggs with runny yolks, cook for about 2-3 minutes, or until the whites are set.
Divide the cooked rice between bowls, then top with the shaved beef, fried egg, cucumber, green onions, and any additional toppings you'd like. Finish with a drizzle of the sriracha mayo and serve immediately.