Chop the celery, onion, and carrots, and slice the new potatoes in half. Set aside.
In a small bowl, combine the softened butter with the thyme, oregano, garlic powder, onion powder, ground black or white pepper, and cayenne pepper. Add enough butter so you have enough for basting. Set aside.
Rinse chicken inside and out, then pat dry with paper towels. (See notes)
Place the chicken breast side down on a board or flat work surface. Cut along both sides of the backbone with a sharp knife or kitchen shears, starting at the thigh end and ending at the neck. Remove the backbone and save it for homemade chicken stock.
Grab hold of both sides of the chicken, and open it like you would a book. Turn it over with the breast side up. Push down on both sides of the breast with your hands until you hear it crack, and flatten the chicken.
Remove the wishbone if desired for easier carving. Rub it inside and out with salt, and let it sit for about 5 minutes to develop the flavors.
Generously rub the chicken inside out with the spiced butter, then optionally marinate in the refrigerator until ready to cook. Thirty minutes is enough, but you could also do this the day before and let it marinate overnight.
When ready to roast, preheat the oven to 400℉ (205℃) and melt the leftover spiced butter.
Place the celery, onions, potatoes, and carrots in the bottom of a Dutch oven, stir in the butter mixture, and put the chicken on top. The juices from the chicken will make the veggies incredibly tasty.
Roast until the skin is crisp and an instant-read thermometer inserted into the thickest part of the breast reads 165℉ (74℃). Start checking around 35 minutes, but it may take longer for larger birds.
Let it stand 5-10 minutes before carving the chicken. Enjoy it with the roasted vegetables and your favorite sides.