Trim the chicken breasts, cutting off any visible fat or ragged pieces. Cut each chicken breast in half lengthwise, trying to make two pieces that are the same size.
Heat the peanut oil in a large heavy frying pan. Season the chicken with fresh ground black pepper, then add chicken pieces to the pan and cook over medium heat until chicken is nicely browned, about 5 minutes on the first side and 4-5 minutes more on the second side.
For best results, turn the chicken when it's browned and use an Instant Read Meat Thermometer to tell when the chicken has reached the safe temperature of 165F/75C.
While the chicken cooks, combine ginger, garlic, peanut butter, rice vinegar, soy sauce, sweetener, and red Thai Curry Paste in a food processor.
Buzz those ingredients together and then taste to see if you want a bit more curry paste.
When the chicken is nicely browned and has reached 165F/75C, remove chicken to a plate and cover with foil to keep it warm.
Reduce heat to low and add the coconut milk, scraping the pan to get off any browned bits.
Stir in curry paste/peanut butter mixture and simmer until it's hot, about 2-3 minutes.
Uncover chicken and stir any juices that have accumulated on the plate into the sauce and simmer another minute or so.
Then turn off the heat and stir in most of the chopped cilantro, saving a little to garnish. Serve chicken hot, with the sauce spooned over.
