How to Make It
Bring a large saucepan of salted water to a boil. Add the potatoes and cook over high heat until tender, about 8 minutes. Drain.
Divide the sausage and onion between 2 large nonstick or cast-iron skillets and cook over high heat, stirring frequently, until the sausage is browned, 8 to 10 minutes. Add the potatoes and thyme to the skillets and season with pepper. Cook over moderately high heat, stirring occasionally, until the potatoes are heated through, about 5 minutes.
Add the eggs to the skillets and season lightly with salt. Cook over moderately low heat, stirring gently, until the eggs are nearly set, about 3 minutes. Add the goat cheese in lumps and fold them in. Sprinkle with the parsley and serve with bread and butter.