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1
Adjust oven rack to lower-middle position and heat oven to 425 degrees.
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2
Mix 3 Tbs. of butter, 1/2 cup of brown sugar, 1 tsp. cinnamon and all the nuts in a small bowl. Spoon a portion of the mixture into each hollowed-out apple core.
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3
For boxed pie crusts, unroll one of the dough sheets onto a floured work surface. Pulling on sides of dough to straighten rounded edges, roll it into an approximate 12-inch square, then cut the dough into four 6-inch squares; brush the perimeter of each square with egg white. Set an apple half on each square. Bring up the 4 corners of dough around the apple and pinch edges to seal. Place on a large (at least 18- by 12-inch) parchment-covered baking dish. Brush dumpling tops and sides with egg white; sprinkle with sugar. Repeat process with remaining apples and dough.
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4
Bake dumplings until pastry sets and starts to turn golden brown, about 10 minutes. Reduce heat to 375 and bake until golden brown, about 20 minutes longer.
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5
While apples bake, bring 1 cup water, the remaining 2 Tbs. butter, 1/2 cup brown sugar and 1 tsp. cinnamon to boil in asmall saucepan over medium heat. Dissolve cornstarch in 2 tsps. water; whisk into hot syrup for a smooth sauce. Cover, keep warm.
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6
For each serving, spoon a portion of sauce on a dessert plate. Set apple dumpling over warm sauce; serve immediately.
