Place chicken, fish sauce, soy sauce, water and white pepper in a zip-top bag and squeeze out as much air as possible. Marinate chicken for 30 minutes and up to overnight, flipping the bag halfway through. If only marinating for 30 minutes, leave the chicken at room temperature. If marinating for longer than 30 minutes, put in the refrigerator but pull it out 30 minutes before frying so the chicken isn't super cold when you fry.
If you want to keep the fried chicken hot while you fry your rice, preheat the oven to 200°F/95°C and you can hold the chicken there once they are fried.
To fry, heat enough oil in a pot to completely cover the chicken (about 2 inches) and bring it to 350°F/175°C. While the oil is heating, transfer the chicken into a mixing bowl and add the cornstarch and flour. Toss until you have a smooth, thin batter, adding more flour if you'd like a thicker coating. When the oil is hot, add the chicken to the oil (don't crowd the pot) and then maintain the frying temperature at about 325°F/165°C. Fry for 8-9 minutes until the chicken is fully cooked.
While the chicken is frying, make sunny side up eggs, 1 per person.