1Thaw pastry sheet. On a lightly floured surface, roll out pastry into a 16"x12" rectangle. Cut into 12 (4-inch) squares. Cover with a dry cloth; set aside.
2Peel apples; cut in half lengthwise. Remove cores; cut lengthwise incisions almost all of the way through each apple half, 1/16 to 1/8" apart. Do not cut all of the way through.
3In a small saucepan, stir jam over low heat until melted. Stir in water, 1 teaspoon at a time, to make a thick puree.
4Place 1 apple half on each square of pastry. Roll up edges slightly, folding in corners to make a bowl-shape around the apple. Brush egg yolk over pastry. Brush apples with warmed jam mixture.
5Preheat oven to 400ºF (205ºC).
Arrange tarts on an ungreased baking sheet; let stand 15 minutes. Bake tarts 20 to 30 minutes or until pastry is golden brown. Cool tarts, then brush with remaining jam mixture. Sprinkle evenly with almond slices.