For the mac, melt the butter in a large saucepan over medium heat. When the butter has melted and started to bubble, whisk in the flour. Cook for 1 1/2 minutes, whisking constantly. Gradually whisk in the milk until no lumps remain. Reduce the heat to medium-low and cook milk mixture, whisking constantly, until it thickens and bubbles, 5-7 minutes.
Remove 1/3 of sauce and save to make dipping sauce.
Remove saucepan from heat and stir in the cheese by the handful, stirring each addition until blended. Stir in the mustard, salt and pepper. Return the sauce to low heat and mix in the pasta until well-coated. Spread the mixture in a single layer on a baking sheet and let cool.
Place a spring roll wrapper on a flat work surface. Brush the edges with egg mixture.