Preheat the oven to 400°Spray a 2 1/2- to 3-quart casserole dish with cooking spray and set aside.
Meanwhile, in a large skillet over medium heat, cook the pancetta, stirring occasionally, until crisp, 13 to 15 minutes. Use a slotted spoon to transfer the pancetta to a bowl or plate. Set aside to cool.
Add the shallots to the pancetta fat and cook, stirring occasionally, for 2 minutes. Add the sweetpotatoes and cook, stirring occasionally, until the sweetpotatoes are al dente, 3 to 4 minutes. Add the broth, figs, thyme, salt, and pepper and bring to a simmer. Remove from the heat and set aside 5 minutes to plump the figs.
Transfer the sweetpotato-fig mixture to a very large bowl. Add the bread and 3/4 of the pancetta, stirring gently to evenly moisten. Add more salt and pepper to taste. Transfer to the prepared casserole dish and sprinkle the remaining pancetta on top. Dot the top with the butter and cover with foil.
Bake until heated through, 30 to 40 minutes. Uncover and bake until browned on top, 5 to 10 minutes.