In a small bowl, mix brown sugar, spices, and butter.
Fill the middle of each apple with the brown sugar mixture. (Any leftover filling can be pressed around the outside of the apples.)
On a lightly-floured surface, roll out each pie crust circle slightly.
Measure and cut a 7-inch square from each crust. This measurement is approximate. Repeat with remaining pie crusts.
Re-roll leftover dough and repeat until you have your seven squares.
Place your filled apples in the center of each square. Lightly brush the edges of each dough square with the egg white and fold up over apples, pleating and sealing to dough.
Place dumplings in your prepared baking dish, not allowing them to touch each other.
Bake on the center rack of your oven for approx. 40 minutes or until pie crust is golden brown.
While dumplings are baking, combine water, cornstarch and sugar in a small sauce pot to make the lemon sauce.
Stir sauce until smooth and cook over medium heat until it comes to a boil.
Boil until it thickens, stirring constantly.
Remove from heat and add butter, lemon juice and lemon zest. Stir to mix.
Remove dumplings from the oven and let them cool slightly.