Prepare the Ingredients: Dice the potatoes into small cubes and slice the leeks thinly. Cut the sausage into bite-sized pieces.
Cook the Potatoes: Heat the olive oil or butter in a large skillet over medium heat. Add the diced potatoes and cook, stirring occasionally, for about 8-10 minutes, until they begin to soften and turn golden brown.
Cook the Sausage: Push the cooked potatoes to one side of the pan and add the sausage pieces. Cook until browned and cooked through, breaking up the sausage into smaller pieces as it cooks.
Sauté the Leeks: Add the sliced leeks to the pan with the sausage and potatoes. Cook for an additional 3-4 minutes, until the leeks soften and release their fragrance.
Add Dijon Mustard: Stir in the Dijon mustard and season with salt and pepper to taste. Continue to cook for 1-2 minutes, ensuring that everything is well-mixed and heated through. Serve: Remove the pan from the heat and serve immediately. Optionally, top with a fried egg for added richness.