Heat half of the oil in a small frying pan, add the sliced mushrooms and season with a pinch of salt and pepper. Fry for 3-4 minutes, turning once or twice until golden brown. Remove from the pan.
Add the remaining oil to the pan, heat on a medium heat, then carefully crack the eggs into the pan. Fry for 3-4 minutes until the white is cooked but the yolk is still runny. Remove from the pan.
Add the spinach, garlic and a pinch of salt and pepper to the pan. Heat through for 1 minute until the spinach is wilted. Turn off the heat.
Divide the boiled rice between two large bowls. Arrange the carrot matchsticks, beansprouts, mushrooms and spinach on top. Place an egg on top of each bowl and pour on the gochujang sauce.