Cut the chicken breast into small pieces. Finely mince the onion.
Heat the oil in a medium skillet, add the onion, and sauté over medium heat.
When translucent, add the chicken and sauté until it changes color.
Add the wine, tomato paste, and soy sauce and simmer until thick, about 1 minute.
Place in a bowl with the rice and mix gently.
In a small bowl, stir 1/2 teaspoon of salt into 1 tablespoon (15 milliliters) of water.
Divide the rice into 4 portions (1/2 cup, 100 grams each) and form into onigiri by dampening your hands with the salt water, scooping the rice into your palm, and quickly but lightly pressing it into a cylinder. Rotate it several times while pressing to make the shape even.
In a small bowl, whisk together the eggs, milk, mayonnaise, and salt and pepper.
Melt the butter in a medium skillet or rectangular Japanese omelet pan.
Pour in half the egg mixture and cook on both sides to form a thin omelet.
Repeat with the remaining egg.
Cut each in half and wrap around the onigiri.