Combine all but the chicken breasts. Taste the marinade and add more dill or rosemary if you wish.
Rub the marinade all over the chicken. If you left the skin on, try to slide your fingers in between the skin and meat and smear the marinade into the resulting pocket.
Let the breasts marinade in a large resealable container or baggie for at least 3 hours.
Fire up the Big Easy fryer. You'll need a bunk bed basket to fit all 4 breasts in at once.
Place 2 breasts in the bottom Big Easy basket and two in the top basket.
Let cook at least an hour (with the top on the Big Easy so the chicken gets good and brown and the skin crisps up nice) before checking the meat temperature, which you want to get to 165 F.
Remove the breasts and let rest until slightly cooled, then slice.