Oahu omelet (Maui omurice) is a dish created by Rick. It has no particular recipe or ingredients, though chicken, eggs, and even rice can be basic components. It's only instruction is that is has to be cooked in a frying pan and the mishmash of ingredients has to be so awful it's difficult to swallow. The purpose of the Oahu omelet is to allow a person to face a challenge.
Rick introduced it to Kuon while Kuon was a teenager living in the United States. Years later in Japan Kuon, under his Ren Tsuruga identity, cooked and ate it with Kyoko. Apart from the challenge, it symbolizes Ren's increasing trust of her and desire to reveal his true self. Also, since Rick told Kuon to have the woman he loves write on the omelet in ketchup to create encouraging magic, Ren's request of Kyoko to do this is yet another indicator of his true feelings for her.
The Oahu omelet is so named because the pronunciation of the Hawaiian city sounds like the English word "awful".