Heat the olive oil in a saucepan over medium heat and fry the onion and mushrooms until soft. Add the garlic and ginger, cook for 1 minute before adding in the gochujang and mirin.
Pour the vegetable stock into the saucepan and bring to a boil. Reduce the temperature and simmer for 5-10 minutes to make a broth.
Meanwhile, place the eggs into a medium saucepan and cover with cold water. Place saucepan over a medium heat and simmer for 4 minutes for soft-boiled eggs. Transfer to a bowl of iced water to cool. Deshell, halve and set aside.
Add the carrots and pak choi to the broth and simmer for 2-3 minutes before stirring in the king prawns.
Heat the cauliflower rice and spoon into warm bowls. Ladle in the vegetable and prawn broth. Top each bowl with a soft-boiled egg and a spoonful of kimchi.