Begin by spatchcocking the chicken (follow the directions and video in the blog article). Season the chicken generously all over, including the underside and beneath the skin. Place the chicken on a baking sheet lined with foil and refrigerate uncovered for at least 4 hours, but up to 48 hours.
Preheat the oven to 400 F.
Heat a big cast iron skillet (at least 11 inches in diameter) over medium heat. Add the neutral oil. Once the oil is heated, place the chicken in the pan, skin side down, and weigh it down with another skillet or heavy pot. Cook the chicken for 10-12 minutes, until it is a deep golden brown.
Remove the pan that was weighting down the chicken and carefully flip it over so that the skin side is now facing up. Arrange the lemon slices around and underneath the chicken. Transfer to the oven and roast for 35-40 minutes, or until the thickest sections of the breasts and legs register 165 F on a meat thermometer.
Remove the chicken from the oven and place on a cutting board to rest. Return the skillet to the burner and cook over medium heat. Add 2 tablespoons cold butter to the pan and use a silicone spatula to scrape away any browned pieces. Once the butter has melted and foamed, add the shallots and simmer for 2-3 minutes, until tender. Add the capers and cook for 1 min.
Simmer the white wine and lemon juice in the skillet. Use a spoon to scrape off any leftover brown pieces in the skillet. Reduce the heat slightly, then whisk in the remaining cold butter, one tablespoon at a time. Whisk frequently until the butter emulsifies into the sauce. Combine the lemon zest and fresh herbs. Season to taste with salt and pepper.
Place the chicken on a serving plate and cover with the lemon caper sauce. Serve immediately.