Mix the shredded cheese, egg, milk, nutmeg, lemon zest and a pinch each of salt and pepper in a bowl to combine.
Turn the oven down to 400*F. Spread the cheese mixture evenly over the puff pastry, leaving a 1-inch border on all sides. Arrange the asparagus and chicken on the tart and then drizzle with olive oil. Layer the parmesan and scallions on the tart and bake until the cheese mixture is slightly puffy, 15 minutes. Let tart rest for 5 minutes before cutting it. Enjoy!