5. Remove the backbone by cutting along each side of it from the neck to the butt. Since you'll be cutting through bones, having a good pair of kitchen shears makes a difference here. Save the backbone and use it for stock later.
6. Using your hands, splay open the chicken. Depending on the chicken, this may happen naturally. Most likely, you will have to remove the breast bone and the cartilage in between. Use the heel of a sharp knife at the neck end of the chicken to make a 1-inch cut on each side of the keel bone. Bend the bird back, splaying it open like a book. Use your knife to cut the membrane along the center of the chicken to expose the keel bone and cartilage. Run your thumbs up and under both sides of the cartilage until it separates from the breast. Gradually pull out the cartilage and keel bone.
7. Flip over the chicken so that it's breast-side up and use your fingers to loosen the skin from the legs, thigh, and breast meat. Spread the herb paste under the skin, spreading it into an even layer by pressing and pushing it around from the top of the skin.
8. Take the hot cast-iron skillet or pan out of the oven and put on the stovetop over high heat.
9. Generously salt both sides of the chicken. Add the remaining 2 tablespoons of oil to the pan and swirl it around to ensure an even coating. Carefully put the chicken in the pan skin-side down and cook it for 3 minutes, then transfer it to the oven.
10. Roast the bird for 30 minutes. To check for doneness, puncture the thickest part of the thigh with a small knife or fork. If the juices run clear, it's done. If the juice is pink, roast the bird for 5 more minutes. If the bird is done, but the skin hasn't crisped up, finish it on the stove over high heat for 2 minutes, then transfer it to a large plate, lightly tented with foil, to rest for 10 minutes.
11. Remove some of the chicken fat to a bowl if there is a lot. Add sliced mushrooms to remaining fat and cook over a medium high heat. Add sprig of thyme and cook until brown and crispy.