Prepare the Rice: Rinse 1½ cups of sushi rice thoroughly under cold water until the water runs clear. This step removes excess starch. Combine the rinsed rice with 2 cups of water in a saucepan and bring it to a boil over medium-high heat. Once boiling, cover the pan and reduce the heat to low. Allow to simmer for approximately 20 minutes or until the rice is tender. Once cooked, fluff the rice with 2 teaspoons of mirin and let it cool.
Mold the Rice: Line a loaf pan with plastic wrap. Pack the cooled rice tightly into the loaf pan. Cover with plastic wrap and chill in the refrigerator for at least one hour. This helps the rice hold its square shape when cooked.
Fry the Rice: After chilling, remove the rice from the pan and cut it into squares. Heat 1 cup of vegetable oil in a deep frying pan or heavy-bottomed pot until it reaches 375°F (190ºC). Fry the rice squares in batches for about 3-4 minutes, or until they become golden brown. Use a slotted spoon to remove them and place them on paper towels to drain excess oil. Cut each square in half for easier serving.
Prepare the Shrimp Salad: In a sauté pan, heat 2 tablespoons of vegetable oil over medium-high heat. Add ¾ pound of large shrimp (peeled, deveined, tails removed) and cook until the shrimp turn pink and opaque, about 2-3 minutes. Remove from heat, chop the shrimp finely, and place them in a mixing bowl. Add ¼ cup of diced green onions, ¼ cup of panko breadcrumbs, 3 tablespoons of kewpie mayonnaise, 2 tablespoons of sriracha, 1 tablespoon of diced jalapeño, and 1 teaspoon of soy sauce. Mix well to combine.
Assemble the Dish: To serve, place the crispy rice squares on a platter. Top each square generously with the spicy shrimp salad. Add slices of 1 medium Hass avocado on top, and if desired, drizzle with 2 tablespoons of eel sauce. Garnish with thinly sliced jalapeño for an extra kick and serve with soy sauce on the side for dipping.