Soak apples in rum for 30 minutes. Drain, reserving rum; cover tightly and set aside.

In small bowl, sprinkle yeast and pinch of sugar over 3 tbsp/45 mL warm water until yeast begins to foam, about 10 minutes. In separate bowl, whisk together cake-and-pastry and all-purpose flours, 2 tbsp/30 mL of the sugar and salt. Scrape yeast into bowl of stand mixer; with paddle, mix in eggs (or by hand, with wooden spoon). Gradually beat in flour mixture until dough is elastic. Beat in butter until thoroughly mixed. Fold in apples.

Scrape batter into well-greased 10-inch/25 cm tube pan, smoothing top. Cover with kitchen towel and let rest in warm place until batter has doubled in volume, about 2 hours. Bake in 400F/200C oven unti skewer inserted in cake comes out clean, about 25 minutes. Run knife between cake and pan; turn cake out onto rack. Let cool. (Make-ahead: Cover and leave at room temperature for up to 1 day.)

Place remaining sugar in saucepan with 1 cup/ 250 mL water; bring to boil and stir until sugar is dissolved. Remove from heat; stir in reserved rum. Place cake on plate; with sharp-tined fork, poke holes all over top of cake. Flip cake over; spoon half of the syrup evenly over cake. Flip and spoon remaining syrup over top of cake, continuing to spoon any syrup on plate until cake has absorbed all the syrup. (Make-ahead: Cover and leave at room temperature for up to 1 day.)

Makes 8 to 12 servings.