Cook the Sausage: In a skillet over medium heat, add the sausages and cook until browned and fully cooked. Break them into pieces with a spatula as they cook.
Sauté the Greens: Once the sausage is cooked, add the olive oil and the greens to the skillet. Sauté for 2-3 minutes until the greens are wilted and tender. Season with salt and pepper, then remove from the skillet and set aside.
Scramble the Eggs: In a bowl, whisk together the eggs and milk or cream (if using). In the same skillet, add a little more oil if needed, and pour in the eggs. Cook gently, stirring frequently, until just set but still creamy.
Combine: Gently fold the cooked sausage and sautéed greens into the scrambled eggs. Adjust seasoning if necessary.
Serve: Plate the scrambled eggs with sausage and greens, garnishing with fresh herbs if desired. Enjoy warm!