Preheat the oven to 350°F (175°C). Prepare the vegetables: peel and chop onion and carrots into medium-large chunks, chop 2 cloves of garlic finely, and trim woody stems off Brussel sprouts and chop any large ones in half, leaving smaller ones whole. Set aside.
Wash and dry the lemon, then grate the peel with a microplane or box grater. Cut the lemon in half. Set aside halved lemon and grated peel.
Remove giblets and untruss chicken, if necessary. Pat chicken dry with a paper towel and season it generously with sea salt, pepper, and grated lemon peel on both sides and in the cavity. Add half lemon, a couple of garlic cloves, and one sprig each of rosemary sage and thyme (or herbs of choice) inside the chicken cavity. If using dried herbs instead, season the chicken on both side and cavity with about 1 tsp of each herb.
In a large Dutch oven or heavy oven-safe pot, melt the butter (or fat of choice) over medium-high heat. Sear the seasoned chicken for a few minutes on each side until golden brown (takes about 2-3 minutes on each side). Remove and set aside.
In the same pot, add the chopped onions, carrots, garlic, and Brussels sprouts, seasoning with salt. Sauté for 3–4 minutes to bring out their flavor.
Add extra herbs and seasoning (if desired) to the veggies. Nestle the chicken into the pot with breast side up, moving the veggies to the side. Add bone broth over the veggies, and squeeze the juice of half a lemon over the chicken. You can also add some lemon slices over the top of the veggies and chicken.
Cover the pot with the lid (or with foil) and place into the preheated oven.
Let the chicken bake for about 1 hour and 15 minutes, or until fully cooked (internal temperature should be 165°F by the thickest part of the thigh, near the bone, and juices should run clear, not pink). For crispier skin, if desired, remove the lid for the last 10–15 minutes of cooking or place under the broiler for 2–3 minutes (watch it closely!).
Remove the pot from the oven and serve right away. You can carve the chicken and stir the shredded meat back in with the veggies, or simply leave it whole and scoop out portions of both chicken and vegetables. Garnish with fresh herbs, sliced green onions, or lemon wedges, and serve with sliced avocado, if desired.