Combine shortening, flour and salt in a food processor, pulsing until it resembles a fine meal. Cut chilled butter into small pieces and pulse a few times. Sprinkle with ice water and pulse until mixture holds together when pinched, adding more water if necessary.

Scrape onto a floured board, form into a ball, wrap with plastic wrap and refrigerate at least 30 minutes.

Preheat oven to 450°F. Peel and core apples. Divide raisins and rum among the core holes and place 1 teaspoon butter into each.

Combine syrup ingredients in a small saucepan, bring to a boil, simmer 3 minutes and set aside.

Divide pastry into 4 parts. Roll each between wax paper into a circle large enough to cover an apple. Encase each apple, pinching and sealing seams with a little water.

Place apples on a baking sheet and brush with syrup. Bake 10 minutes at 450°F. Reduce heat to 330°F, brush again, and bake 35 minutes more, brushing every 10 minutes.

Cool 5 minutes and serve hot or at room temperature.