Trim the Brussel sprouts by removing the tough outer leaves and stems. Halve lengthwise. Cook the Brussel sprouts in a cast iron casserole or oven-proof skillet in boiling salted water for 8 to 10 minutes. Drain and set aside.
Peel the onion, cut through the stem into 6 equal wedges, and trim any ragged tops. Wipe dry the casserole dish and heat 1/4 cup oil in it. When the oil is hot but not smoking, add the onions. While the onions are cooking, halve the parsnips lengthwise, then in bite-size wedges and add to the onions. While the parsnips and onions are cooking, cut the carrots and celery in the same manner as the parsnips and add to the vegetables already cooking in the casserole dish. Continue cooking the vegetables until lightly browned on all sides, 1 to 2 minutes, turning as needed. Add the cooked Brussels sprouts to the dish. Season with salt, to taste. Cook until all the vegetables are well browned, about 10 minutes, turning as needed. Remove the vegetables to a bowl and season with 2 tablespoons of Fennel Spice Rub to coat. Remove the vegetables from the casserole dish and set aside.
Preheat the oven to 425 degrees F.
Cut the chicken into bone-in serving pieces (2 drumsticks, 2 thighs, and 8 half pieces of breast). Heat the remaining 1/4 cup of oil in the casserole dish over high heat. Season the chicken pieces well on both sides with the remaining Fennel Spice Rub. When the oil is hot but not smoking, add the chicken pieces skin side down, in batches if necessary. Cook until the chicken is dark brown on all sides, about 12 to 15 minutes. Remove the chicken from the dish. Tilt the pan and pour off all but 2 tablespoons of fat. Reduce the heat to medium, add the garlic and pancetta, and cook until golden, about 1 to 2 minutes.
Add the beans and their liquid into the casserole dish with the pancetta. Bring to a simmer. Add the reserved vegetables and the chicken, skin side up. Roast, uncovered, until the chicken is fully cooked and the surface is nicely browned, 25 to 30 minutes. Let rest at room temperature for 10 to 15 minutes before serving warm.
Put the fennel seeds, coriander seeds, and peppercorns in a heavy pan over medium heat. Watch carefully, tossing frequently so the seeds toast evenly. When light brown and fragrant, pour the seeds onto a plate to cool. They must be cool before grinding, or they will gum up the blades.
Pour the seeds into a blender and add the salt. Blend to a fine powder, shaking the blender occasionally to redistribute the seeds. Store in a tightly sealed glass jar in a cool, dry place, or freeze.