Pat the chicken dry with paper towels. Heat the neutral oil in a large skillet or wok over medium-high heat. Add the chicken in a single layer, working in two batches if needed, and brown for 3 to 4 minutes per side. Transfer the browned chicken to a plate.
Reduce the heat to medium. Add the shallots, garlic, ginger, and dried chiles, if using, to the skillet. Cook for 2 to 3 minutes, stirring often, until the shallots begin to soften and the aromatics smell fragrant.
Stir in the soy sauce, rice wine or dry sherry, toasted sesame oil, brown sugar, and water. Scrape up any browned bits from the bottom of the skillet.
Return the chicken and any juices on the plate to the skillet. Bring the liquid to a gentle simmer, then reduce the heat to medium-low. Cover and cook for 10 minutes.
Uncover and simmer for 5 to 7 minutes, stirring occasionally, until the chicken is cooked through and the sauce has reduced to a glossy coating. The thickest chicken pieces should reach 165°F (74°C) on an instant-read thermometer.
Remove the skillet from the heat and stir in the Thai basil just until wilted. Taste and add a small splash of water if the sauce seems too salty or concentrated. Serve hot with steamed rice.