Submerge cubed sweet potatoes in salted water in a large saucepan and bring to a boil. Reduce to a simmer and simmer until tender, about 8-10 minutes. Drain and return to the saucepan. Mash until smooth. Season with salt and pepper and set aside.

Meanwhile, heat just half of the oil in a large ovenproof skillet over medium heat. Add the green beans, cover, and cook until tender, about 5 minutes. Transfer the green beans to a plate and set aside.

Add the remaining oil to the same skillet over medium-high heat. Add the ground chicken and cook, breaking it up into pieces with a spoon. Once browned, add the broth, Worcestershire sauce, and thyme. Stir to combine.

Bring the chicken mixture to a simmer and simmer until the sauce reduces slightly. Stir in the green beans. Season with salt and pepper.

Spoon the mashed sweet potatoes on top and spread to cover the filling. Broil until the filling is bubbling and the sweet potato is golden. Serve.