Melt the butter in a large pot over medium-high heat, add the leeks and cook until soft and golden around the edges, 5-7 min. Add the cabbage and garlic and cook, stirring occasionally, until cabbage begins to caramelize about 10 min.
2
Stir in potatoes, stock 4 cups water, salt and thyme. Bring soup to a simmer and cook, partly covered, until potatoes begin to fall apart, 45 to 50 minutes. Add more water, as needed, to reach the desired consistency. Season with black pepper and serve, topped with cheese.