Preheat oven to 400°F (200°C). Lightly spray 2 (13x9-inch) baking pans with cooking spray. (See Note.) Line pans with parchment paper, letting excess extend over sides of pans.

In a medium saucepan, melt butter over medium heat. Add ½ cup (120 grams) water, milk, sugar, and salt; bring to a boil. Using a wooden spoon, stir in flour. Cook, stirring constantly, until a skin forms on bottom of pan, 1 to 2 minutes. Transfer mixture to the bowl of a stand mixer fitted with the paddle attachment. Beat at low speed until dough is just warm to the touch, about 1 minute. Add eggs and egg white, one at a time, beating until combined after each addition. Divide batter between prepared pans (about 1½ cups or 362 grams each).

Bake, one batch at a time, until fully puffed and deep golden brown, about 20 minutes. Let cool in pan for 5 minutes. Remove from pan, and let cool completely on a wire rack.

Spread Maple Mousseline on 1 pastry in an even layer. Top with remaining pastry, and refrigerate until mousseline is set, about 1 hour. Garnish with maple syrup, if desired. Serve immediately, or refrigerate until ready to serve. Best served same day.