Soak the vermicelli in a large bowl of warm water.
Submerge two sheets of rice paper in water for around 2 seconds. Then, place them on a flat surface and allow it to sit for about 30 seconds, at which point they will start to soften.
Fold the sides so that they meet in the center. Then, roll from the bottom up until you have a cylinder.
Repeat step 2. Then, place some cheese in the center of the sheets. Fold the sides over the cheese and then roll from the bottom up until you have a very fat cylinder.
Repeat same steps for fried seaweed.
Repeat step 2 and place some soaked vermicelli, lengthwise, in the center of the rice paper. Fold the sides over the noodles and roll from the bottom up. In the end, I had 3 cheese stuffed rice cakes, 2 seaweed stuffed rice cakes, and 2 vermicelli stuffed rice cakes (I reserved some vermicelli for the end).
To a large pan, add the vegetable stock, soy sauce, gochugaru, gochujang, garlic, and onions and bring the mixture to a boil.
Add the rolled rice sheets and leftover vermicelli to the boiling vegetable stock and cook for about 10 minutes, until the rice cakes are tender and the sauce is thick.