Rub the entire chicken with the lemon halves, squeezing the juice out as you go. Combine 3 tbsp. olive oil with salt and pepper in a small ramekin. Cover all sides of the chicken with the olive oil/salt and pepper mixture, using a pastry brush. : let the chicken rest for 1 hour.

Preheat oven to 400 degrees F. Heat 3 tbsp. of olive oil over medium-high heat in a cast-iron skillet. Once the oil is hot, place both halves of the chicken in the skillet, skin-side down down and sear for 7-10 minutes, until the skin is brown, crispy and loosens from the pan on its own.

Once you've finished searing, flip the chicken over, and add the sliced garlic, cubed butter, sage leaves and a splash of the chicken broth to the skillet and place the entire skillet in the oven. Roast the chicken for 25 minutes, basting every 7 minutes or so. Internal temperature should read 165 degrees F.

while the chicken is roasting, whisk together the chicken broth, lemon juice, balsamic vinegar, brown sugar and cornstarch. Set aside.

For darker, crispier skin, baste the chicken with drippings from the pan and set it under the broiler for an additional 5 minutes. Rotate the skillet half-way through so the skin crisps evenly. Watch it closely so it doesn't burn!

When the chicken is done roasting/broiling, remove it from the skillet, and transfer it to a casserole dish (you can keep it in the oven on the warm setting). Put the skillet back on the stove burner and turn the flame on medium-low. Pour the sauce mixture into the skillet and use a whisk to loosen up any bits from the bottom of the pan (this is called de-glazing). Let the sauce simmer for 5-7 minutes.

Remove the sauce from heat, and spoon some of the sauce over the chicken. Reserve some sauce to serve on the side. Garnish with lemon wedges and a few sage leaves. Serve with a vegetable of your choice.