Saute the onion in oil in a heavy-bottomed saucepan over medium-high heat, until softened. Stir in the tomato sauce, brown sugar, apple cider vinegar, salt and pepper. Let simmer for 15 minutes.
Heat the oil in a heavy-bottomed saute pan over medium-high heat. Add the pork and brown. Once browned, add the garlic, onion, celery, and green bell pepper. Cook until softened, about 5 minutes. Season with salt and pepper, to taste. Add the chicken broth and cayenne. Stir in the cooked rice and parsley, mixing thoroughly and letting the broth reduce until there is no moisture left in the pan. Taste and season with salt and pepper, if necessary.
In a large pot of boiling salted water, over medium heat, add the collard leaves and cook until tender, about 5 minutes. Drain and rinse with cold water.
Lay a collard leaf out on a flat surface and add 1/4 cup of the dirty rice into the center. Fold both the sides into the center and the top and bottom over the center. Roll into a cylinder and repeat with the remaining leaves. If there are any remaining leaves you can chop them up and add to the sauce.
Pour a 1/2-inch layer of sauce into a 13 by 9-inch casserole dish. Arrange the collard rolls, seam sides down, on top of the sauce. Pour the remaining sauce over the stuffed collards and cover with foil. Bake in the preheated oven for 40 minutes. Remove from the oven and serve.