Preheat your oven to 375°F (190°C).
Prepare the leeks by thoroughly rinsing and slicing them.
Sauté the leeks in a skillet over medium heat until softened, about 5-7 minutes.
Add the salmon to the skillet and cook for an additional 5 minutes until just cooked through.
In a mixing bowl, combine the sautéed leeks and salmon with cream cheese, dill, salt, and pepper.
Prepare the phyllo pastry on a clean work surface, layering 4 sheets together.
Cut the layered phyllo into 4-inch squares and press them into a muffin tin.
Fill each phyllo cup with the salmon and leek mixture, and top with a drizzle of beaten egg.
Bake in the preheated oven for 20-25 minutes, or until golden and crisp.
Let the tartlets cool for a few minutes before serving.