Preheat the oven to 400ºF. Wash the sweet potatoes, pat them dry, and prick their skins a few times with a fork. Slice the sweet potatoes in half lengthwise, then place them on a baking sheet. Drizzle the cooking oil over the potatoes, then use your hands to smear the oil over their entire surface (skin and cut sides), leaving a liberal amount of oil on the baking sheet under the potatoes to keep them from sticking.
Place the sweet potatoes with the cut side up, then sprinkle with cinnamon, a pinch of cayenne pepper, and a pinch of salt. Flip the sweet potatoes over so they are cut side down, then roast for 45-50 minutes, or until they are soft all the way through and the juices are caramelized and bubbling out of the holes in the skin.
While the sweet potatoes are roasting, prepare the chicken and green beans. Combine the spices for the chicken in a small bowl (smoked paprika, brown sugar, garlic powder, cayenne, salt, and freshly ground pepper-about 20 cranks of a pepper mill).
Pat the chicken dry, then sprinkle the spice rub over both sides. Heat a large skillet over medium, then add the cooking oil and swirl to coat the surface. Add the chicken and cook until they are deeply browned on each side and the internal temp has reached 165ºF. Remove the chicken to a cutting board and let it rest.
While the chicken is cooking, prepare the green beans. Add about one inch water to a sauce pot and place a steaming basket in the pot. Add the green beans to the basket, place a lid on top, and place them over medium-high heat. Allow the water to come up to a boil and steam the green beans for 7-10 minutes, or until they are bright green and only slightly softened.
Remove the green beans from the pot, pour out the water, and place the beans back in the pot without the steaming basket. Add 1 Tbsp butter and allow the residual heat from the beans to melt the butter. Stir to coat, then season with a pinch of salt and pepper.
Slice the chicken breasts into strips. Divide the sweet potato halves, green beans, and chicken between four containers or plates. Serve immediately or refrigerate and reheat later.