Heat a large saute pan over medium high heat and melt a thin layer of clarified butter. Add the potatoes and ¾ teaspoon of salt and cook, stirring occasionally, until the potatoes begin to soften, 8 to 10 minutes.

Meanwhile, start cooking the sausage either in a separate medium saute pan over medium heat (with a tablespoon of clarified butter or olive oil) or on the outdoor grill. Cook until the sausage is brown all the way through, about 5 or 6 minutes on each side.

Add the sliced cabbage to the pan with the potatoes and cook for 1 more minute. Pour in the broth, cover with a lid, and cook while stirring occasionally until the cabbage has softened, about 5 minutes.

Meanwhile, if topping this dish with fried eggs, start another medium saute pan over low heat and melt a tablespoon of butter. Carefully crack the eggs into the pan without overlapping them, season with a little salt and pepper, and let them cook undisturbed for a couple minutes until the white part of the egg is almost completely opaque. Carefully flip over the egg and cook for another minute or two (still on low) or until the yolk is the desired doneness.

Divide the potato and cabbage mixture evenly among 4 big bowls, top each with a link of sausage, and then sprinkle with the watercress (or arugula) leaves. Carefully place a fried egg on top and serve warm.