Trim any visible fat from the chicken breasts and cut each breast in half lengthwise so you have eight pieces of roughly equal thickness.
Season the chicken pieces with fresh ground black pepper.
Heat about 2 tablespoons peanut oil in a large heavy frying pan over medium heat.
Add the chicken to the hot pan and cook until nicely browned, about 5 minutes on the first side and 4–5 minutes on the second side, or until an instant-read thermometer registers 165°F (75°C).
While the chicken cooks, combine minced ginger, minced garlic, peanut butter, rice vinegar, soy sauce, sweetener, and red Thai curry paste in a food processor and blend until smooth; taste and add more curry paste if desired.
When the chicken reaches 165°F (75°C), transfer it to a plate and tent with foil to keep warm.
Reduce the pan heat to low and pour in the can of unsweetened coconut milk, scraping the pan to release any browned bits.
Stir the blended peanut-curry mixture into the coconut milk and simmer gently until the sauce is hot and slightly thickened, about 2–3 minutes.
Uncover the chicken and add any juices on the plate into the sauce, simmering another minute to combine.
Turn off the heat and stir in most of the chopped cilantro, reserving a little for garnish.
Serve the chicken hot with the peanut-coconut sauce spooned over and garnish with remaining cilantro if desired.
