Heat a large Dutch oven over medium-high heat and add the sausage.
Cook, stirring occasionally until the sausage is caramelized and the fat is rendered, 4 to 6 minutes.
Add the onions and celery and cook, stirring occasionally, until vegetables are soft and lightly browned, about 4 minutes. Add the garlic and cook, stirring, for 1 minute.
Add the cider and cook until almost completely reduced. Add the sauerkraut, broth, potatoes, thyme and pepper and bring to a boil.
Reduce the heat to a low simmer and cook, stirring occasionally, until potatoes and sauerkraut are very tender and the broth is flavorful, about 1 hour. Taste and adjust the seasoning, if necessary.