Heat a large wok or skillet over medium heat. Add neutral oil, then add thinly sliced scallions, chopped cloves of garlic, Thai chiles, and chopped shallots. Cook, stirring occasionally, until fragrant.
Add ground chicken, then cook, breaking up with a spatula, until mostly cooked through.
When the chicken is almost fully cooked, add the sauce ingredients: low-sodium soy sauce, dark soy sauce, oyster sauce, fish sauce, and brown sugar. Stir until the sugar has dissolved and the chicken is coated evenly in sauce. Stir in fresh basil leaves and cook.
Serve generous spoonfuls of the Thai basil chicken over steamed Jasmine rice. Top each portion with 1 fried egg (I recommend a runny yolk, but cook it to your preferred doneness), thinly sliced scallions, and a little extra fresh basil. Enjoy immediately!