Process the lemongrass, shallots, garlic, fish sauce, brown sugar and red pepper flakes in a food processor until it turns into a paste. Place the butterflied chicken breasts and the paste in a resealable plastic bag. Massage the bag to combine the chicken and the paste. Refrigerate and marinade for 1 hour up to overnight.
In a large skillet, heat the oil over medium heat. Remove the chicken from the marinade and scrape off any excess marinade on the chicken. Discard the marinade.
Cook the chicken breasts, flipping halfway through, until golden brown and no longer pink inside, about 8-10 minutes total.
Season with salt and pepper to taste. Serve with lime wedges and garnish with parsley.