Tteokbokki: Spicy Korean Rice Cakes

Name: Tteokbokki: Spicy Korean Rice Cakes
Ingredients: 1 oz. dried anchovies, gutted (about 40 small anchovies); 6 c. water; 12 dried shiitake mushrooms; 6 square piece dried kelp; 3/4 tsp. kosher salt; 1 lb. Korean rice cakes; 1 tbsp. grapeseed oil; 1 tbsp. gochugaru (Korean red chili pepper flakes); 1/4 c. gochujang (Korean red chili pepper paste); 2 large cloves garlic, minced; 1 tsp. low-sodium soy sauce; 2 tsp. white vinegar; 1 tbsp. honey; 2 to 3 c. anchovy broth, divided; 6 oz. Korean fish cakes, cut into bite-sized triangles; 3 green onions, sliced into 2 pieces, plus more for garnish; 1 tsp. toasted sesame oil; Toasted sesame seeds, for garnish