Preheat the oven to 400℉.
Spread the sweet potatoes evenly over a rimmed baking sheet. Bake for 45-55 minutes, until the potatoes are soft when pinched (wear an oven mit!).
While the potatoes are in the oven, place the chicken in a large pot and add water to cover. Bring to a simmer over medium heat. Cover and simmer for 15-20 minutes, until the chicken pulls apart easily with a fork. Remove the chicken from the pot and transfer to a large bowl and shred the chicken.
Pour ½ cup BBQ sauce over the shredded chicken. Toss to combine.
Remove the sweet potatoes from the oven and set aside to cool. Reduce the oven to 350℉.
Peel the sweet potatoes and add them to a large bowl. Add the butter, salt, and pepper and mash well. Spread the sweet potatoes over the bottom of a 9-in square baking dish.
In a 10-inch skillet, heat the olive oil. Add the collard greens and toss to coat. Cover and cook for 4-5 minutes, until the collards have wilted and reduced in size. Squeeze the lemon juice over the collard greens, toss them one more time, then spoon over the mashed potatoes.
Spread the BBQ chicken over the collards and bake for 20-25 minutes, until the top is browned.
Drizzle the remaining BBQ sauce over the casserole, garnish with diced red onion and parsley, and enjoy!