Pour the chicken broth into a medium saucepan and bring to a simmer over medium heat. Reduce the heat to low and keep warm.
Heat the olive oil in a medium Dutch oven or sauté pan over medium heat. When the oil is hot and shimmering, add the onion, apple, garlic, and thyme. Cook for about 3 minutes until the onion is translucent and the apple is softened slightly. Add the sausage to the pan and cook, breaking up the meat into small pieces with a wooden spoon or spatula, until no longer pink, about 5-7 minutes.
Stir in the Arborio and cook for 2 minutes to lightly toast the grains. Add the wine and cook, stirring regularly, until the liquid has been absorbed, about 2 minutes.
Add 1 cup of the warm stock to the pan. Reduce the heat to low and cook gently (the liquid should be just simmering), stirring periodically, until the liquid is almost completely absorbed. (This should take about 5-7 minutes.) Continue adding broth, ¾ cup at a time, until the rice is tender and creamy.
When the last addition of broth is almost absorbed (you still want there to be some liquid in the pan), stir in the Parmesan and half of the goat cheese. (If the risotto is too thick after adding the cheese, you can always add a splash more chicken broth.) Season with salt and white pepper to taste.
Divide the risotto among four plates or bowls and crumble the remaining goat cheese on top. Serve immediately.