Note: The dough needs to chill for at least 45 minutes before rolling, so plan ahead. Good apple varieties include Golden Delicious, Jonagold, Jonathan, Braeburn or Ida Red. Cane sugar is a particularly nice, caramel-like brown sugar, available at most groceries.
• 11/4 c. all-purpose flour
• 2 tbsp. granulated sugar
• 1 tsp. baking powder
• 1/2 tsp. salt
• 5 tbsp. cold unsalted butter, cut in 1/2-in. pieces
• 2 tbsp. vegetable shortening, such as Crisco
• 1/2 c. buttermilk
• 1/4 c. brown sugar, packed (see Note)
• 1/2 tsp. cinnamon
• Pinch of freshly grated nutmeg
• 1 tbsp. unsalted butter, room temperature
• 4 apples, no larger than 3 in. in diameter
• 1 egg white, slightly beaten
• Decorative, or sparkling, sugar
In medium bowl, whisk together flour, granulated sugar, baking powder and salt. Add butter and shortening and, with a pastry blender or your fingertips, work the butter into the flour mixture until it resembles small crumbs.
Add the buttermilk and stir until it comes together in a soft dough. With your hand, knead and squeeze the dough a few times in the bowl until it holds together. Shape it into a disc, wrap in plastic wrap and place in refrigerator to chill for at least 45 minutes. Overnight is OK, too.
In a small bowl, mix together the brown sugar, cinnamon and nutmeg. With your fingertips, work in the butter until crumbly. Set aside.
Preheat the oven to 425 degrees. Remove dough from refrigerator to take off the chill.
Peel the apples, then using a melon baller (or working carefully with a paring knife and small spoon), remove the core and seeds from each apple, being careful not to go all the way through. Remove the blossom end from the bottom of each apple. Place one-quarter of the filling in each apple. Set aside.
On a lightly floured surface, roll out the pastry dough to a 13-inch square, checking often under the dough to make sure it's not sticking and adding a bit more flour as needed.
Using a ruler and a knife or pizza cutter, cut the dough into 4 (6-inch) squares. Reserve the dough remnants.
Place an apple in the center of a pastry square. Lightly brush the edges with the beaten egg white. Bring each corner up to the top of the apple, trying not to stretch it too much. Press corners together to secure, then pinch the seams to enclose the apple. Repeat with remaining apples.
Set dumplings on a rimmed sheet pan. With a paring knife, cut leaf shapes from the dough remnants, using the blade to make vein lines. Attach two leaves to each dumpling, then brush with remaining egg white and sprinkle generously with sparkling sugar.
Bake for 20 to 30 minutes, checking the apples' doneness after 20 minutes by inserting a small knife into the dumpling. The apples don't need to be soft, but there should be some "give." Bake until golden and the apples are tender.
Serve warm with ice cream, whipped cream or crème fraîché. Add a drizzle of caramel syrup, if desired.