Prepare rice according to package directions; set aside.
Meanwhile, heat 2 tbsp vegetable oil in large skillet set over medium heat; cook onions for 3 to 5 minutes or until softened. Add beans, garlic, aji amarillo paste, salt, pepper, cumin and oregano; cook for 3 to 5 minutes or until fragrant.
Combine cooked rice with bean mixture. Divide mixture evenly into two portions.
Heat 2 tbsp oil in 8-inch nonstick skillet set over medium heat; add 1 portion of the rice mixture to skillet. Press down to flatten evenly into 1/2-inch thick patty. Cover and cook for 8 to 10 minutes or until bottom is golden and crisp. Turn off heat; remove lid. Gently run spatula around edge; shake skillet to loosen bottom. Hold large flat plate upside down over skillet. Carefully, yet quickly, invert cake in skillet onto plate (cake should be browned-side up). Repeat with remaining oil and rice mixture.
Meanwhile, heat 2 tbsp oil in medium skillet set over medium heat; fry eggs sunny-side up. Arrange egg and avocado slices over rice cakes; scatter pickled red onions over top. Garnish with cilantro.
Serve with sliced steak, shrimp, or fried plantains.