Step 1: Peel and core the apples.
Step 2: Slice horizontally (so they look like pineapple slices). There should be about 14-16 slices.
Step 3: Heat 1/4 cup corn syrup in skillet.
Step 4: Place half of apple rounds in skillet.
Step 5: Sprinkle with 2 tablespoons brown sugar.
Step 6: Cook, uncovered, over low heat until tender, turning to brown both sides. Keep intact if possible.
Step 7: Remove and cool.
Step 8: Repeat with remaining corn syrup, apple rounds and brown sugar.
Step 9: Sift flour, salt and nutmeg together.
Step 10: Cut in butter until particles are the size of small peas.
Step 11: Combine eggs, milk, and almond extract.
Step 12: Sprinkle egg mixture over flour mixture, a little at a time, while stirring lightly with fork.
Step 13: Add just enough egg mixture to make a dough that will hold together.
Step 14: Reserve remaining egg mixture for top.
Step 15: Wrap dough and refrigerate about 1 hour.
Step 16: Preheat oven to 450°F.
Step 17: Divide dough in half.
Step 18: Form each half into a ball and flatten to about 1/2" thickness. Smooth edges.
Step 19: Place one portion of dough on a lightly floured board and roll out to 1/16" thickness.
Step 20: Cut out circles 1/4" larger than apple rounds.
Step 21: Place on ungreased baking sheets.
Step 22: Top each circle of dough with an apple round.
Step 23: Combine sugar and cinnamon.
Step 24: Sprinkle 1/2 teaspoon on top of each apple. Reserve remainder.
Step 25: Roll out remaining dough and cut in circles 3/4" larger than apple rounds.
Step 26: Cut a round out of the center of each circle so that it resembles a doughnut.
Step 27: Place "doughnuts" over apple rounds.
Step 28: Crimp edges with fork to seal.
Step 29: Place about 1 teaspoon of jam in center of each top circle.
Step 30: Brush with remaining egg mixture and sprinkle with remaining cinnamon sugar.
Step 31: Bake until golden brown, 10-15 minutes.
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