Preheat oven to 450 degrees F with a rack in the upper third of oven.
Place shallots, radishes and/or turnips, sweet potato, fennel, carrots, and 4 sprigs thyme on a sheet pan. Drizzle with olive oil and season with salt and pepper. Toss well to coat.
In a small bowl, combine 2 tablespoons salt and 1 tablespoon pepper. Dry chicken thoroughly with paper towels. Using your fingers, slide beneath skin of breast, thighs, and drumsticks, to ease in seasoning. Push slices of butter under breast of chicken. Season chicken thoroughly with salt and pepper mix, being sure to season under the skin of the breast and legs, inside the cavity, and on the underside of the bird. Stuff garlic and remaining thyme sprigs in the cavity.
Place chicken on top of vegetables on sheet pan and transfer to oven.
Roast until vegetables are charred and chicken is cooked through and crispy, about 1 hour 10 minutes, rotating sheet pan and flipping vegetables halfway through roasting. Serve with lemon wedges.