Combine the figs, honey and lemon juice in a large bowl; add 3 cups warm water. Cover with plastic wrap and set aside until the figs are tender and soft, 20 to 25 minutes. Pour off the liquid into a separate bowl; set aside.
Make the stuffing: Heat the olive oil in a large skillet over medium heat. Add the onions and rosemary and gently saute until translucent, about 4 minutes. Add the sausage and saute until browned, 10 to 12 minutes. Scrape the sausage mixture into the bowl with the figs. Add the cornbread pieces and season well with salt and pepper. Give it a good toss until it's well combined. In a separate bowl, whisk the eggs, heavy cream and 1/2 cup stock; pour over the cornbread-sausage mixture and stir to combine, adding up to 1/2 cup more stock if the mixture is dry. Set aside while you work on the turkey.
Preheat the oven to 350 degrees F. Rinse the turkey thoroughly inside and out with cold water and pat dry with paper towels. Using your fingers, gently lift the skin from the turkey breast and massage the 1 stick softened butter onto the breast meat. Sprinkle the cavity and skin liberally with salt and pepper. Stuff the bird with the cornbread stuffing. Cross the legs over each other and tie with kitchen twine. Put the turkey on a rack in a large roasting pan and place it in the oven. Roast 2 hours.
Meanwhile, make the glaze: Bring the reserved fig liquid to a simmer in a small saucepan over medium heat; cook until reduced by half, 10 to 12 minutes. Add the balsamic vinegar and cook until syrupy, about 8 more minutes. Cut up the remaining stick of butter and whisk it into the glaze.
After the turkey has roasted 2 hours, baste it with the fig glaze and continue roasting until a thermometer inserted into the meaty part of the thigh registers 170 degrees F, 30 minutes to 1 hour more. (If the legs or breast brown too quickly during roasting, cover them with foil.) Transfer the turkey to a platter or cutting board, loosely cover with foil and let rest up to 30 minutes before carving. Garnish with rosemary sprigs.