First, butterfly the chicken. Using heavy shears or a knife, cut down close to the backbone on each side, and remove the bone. Place the chicken skin side up on a flat surface and press with a heavy pan (or a fist) to flatten. Set aside.
Position oven rack about 6-8" from the broiler heating element. Preheat the broiler to high.
Rub the chicken with 2 teaspoons of olive or vegetable oil. Place skin side up on a baking sheet lined with aluminum foil (this makes it easier to clean later) and broil for 5 minutes. Check to make sure the chicken is browning nicely, baste with oil dripping and continue broiling for another 5 minutes or so, until you get a beautiful deep golden brown color.
Remove the chicken from the oven, season with salt and pepper all over and set aside.
In a large sautee pan with a lid, heat the oil and the butter over medium-high heat. Add the onions, the broth and the herbs, and sautee for about a minute. Drop the heat to low, place the chicken in the pan skin side up, cover with a lid and fry for about 20-30 minutes, until the internal temperature in the thickest part registers 160F, basting with pan juices 2-3 times during cooking.
Transfer the chicken to a serving platter and let rest for 5 minutes, then carve, pour the pan sauce over the chicken and serve.