Prep the Ingredients
If using frozen rice cakes, soak your rice cakes in a bowl of cold water to help break them apart. If using fresh rice cakes that are a little dry or a few days old, you can also soak them to help soften them up.
Slice green onions into three sections lengthwise (separate the green tops and white stems). Then, thinly slice the white stems lengthwise. Reserve half of the green tops and slice them diagonally to use for garnish.
Slice your yuba into small squares, then into triangle shapes to resemble fishcakes.
Prepare the Tteokbokki Sauce
In a small bowl, mix gochujang, gochugaru, coconut sugar, gluten-free soy sauce, and toasted sesame oil to form a paste.
Assemble the Vegan Tteokbokki
Add water to a saucepan or pot, along with shiitake mushrooms and kelp. Bring to a low simmer and cook for about 15 minutes. Remove the mushrooms and kelp and set aside (you can use add these, thinly sliced, back into the dish later or just discard).
Drain your rice cakes and add them to the pot along with the yuba, green onion stems, and green tops. Bring the mixture to a low boil.
Add in your seasoning paste and gently stir in to make sure it fully dissolves. Continue to cook until the sauce thickens, stirring occasionally. After about 10 to 15 minutes, the sauce should be nice and glossy, and the rice cakes are cooked through.
Garnish with sliced green onions and sesame seeds if desired, and enjoy immediately.