Lay thawed puff pastry flat on a floured surface. Roll out into a rectangle. Transfer onto a parchment-lined baking sheet and use a fork to prick dough everywhere except outer border (that will be the puffed crust).
Whisk together one egg with one tablespoon of milk. Use a brush to paint egg wash onto the border of pastry dough.
Drizzle balsamic reduction over center of the puff pastry. Top with minced shallot, then Gruyère and Havarti.
Lightly coat asparagus with olive oil, salt and pepper. Layer on top of cheese.
Bake for 15-18 minutes. Pull pastry out when golden brown color.
Garnish with flaky salt, freshly cracked black pepper and freshly grated Pecorino Romano cheese.