In the same skillet, stir in the onion, sweet potatoes, thyme, 1/4 teaspoon of salt, and 1/4 teaspoon of pepper, and cook for 3-5 minutes, until the onions are soft. Pour in 1/2 cup of the chicken broth and cover. Cook 5-7 minutes, stirring occasionally, until the sweet potatoes are tender. Uncover, and add the last 1/2 cup of chicken broth. In batches, add the kale, and toss to incorporate. Cook until the kale is wilted and tender and the liquid has almost evaporated. Return the sausage to the skillet and stir. Cook until heated through, 1-2 minutes.