Korean Dduk Guk Rice Cake Soup

Name: Korean Dduk Guk Rice Cake Soup
Ingredients: 4 cups to 5 cups rice cakes (fresh ones are often found around the holidays near the register of your local Korean market; otherwise bagged fresh or frozen is fine); 1/2 pound ground beef; 2 teaspoons vegetable oil, divided (1 teaspoon for beef + 1 teaspoon for egg jidan); 1 tablespoon minced garlic; 1 pinch kosher salt and freshly cracked black pepper; 10 cups cold water (you can always add more); 5 eggs, divided (3 eggs, lightly beaten + 2 eggs, separating whites and yolks); 5 scallions, divided (4 cut into 1-inch diagonal chunks + 1 chopped finely for garnish); 1 teaspoon toasted sesame oil; 1 tablespoon Korean soup soy sauce (gukganjang), more to taste; 2 to 3 sheets large sheets of unseasoned nori seaweed, cut by scissor into matchstick-ish size (to match the jidan), and put in a small bowl; More Korean soup soy sauce, soy sauce, or kosher salt, and freshly cracked black pepper, sesame oil to taste