Cut the sweet potatoes into ½-inch pieces. Transfer to a small saucepan, cover with water, and bring to a boil. Reduce heat to medium and simmer for 4–6 minutes, or until just fork-tender. Drain and set aside.
While the sweet potatoes cook, heat the olive oil in a large, deep skillet over medium heat. Add the peppers and onions, season with salt and pepper, and cook for about 5 minutes, stirring occasionally, until slightly softened.
Add the drained sweet potatoes to the skillet. Season with additional salt and pepper as needed and cook for 3–5 minutes, until the potatoes are tender and the peppers and onions are cooked through.
Push the sweet potatoes, peppers, and onions toward the edges of the skillet. Add the butter to the center, then add the ground turkey once the butter has melted.
Season the turkey with salt, pepper, garlic powder, oregano, basil, and red pepper flakes. Cook for 4–5 minutes, breaking it into small pieces with a wooden spoon or spatula, until fully cooked through and no longer pink.
Stir everything together, then add the chopped kale and chicken stock. Reduce the heat to low, cover, and cook for 5–7 minutes, stirring occasionally, until the kale is wilted and tender.
Increase the heat to medium. Stir in the fresh garlic and cook for about 1 minute, until fragrant.
Remove from the heat and top with crumbled goat cheese before serving.