In a bowl, whisk together the flour, sugar, cinnamon, cardamom, clove and salt.
In a large bowl, whisk together the egg yolks, butter, and vanilla. Mix in a third of the flour mixture, then a third of the beer to combine. Add the rest of the flour mixture and beer in two additions; whisk well to combine. Set aside for 30 minutes.
Peel, core, and slice the apple into ten 1/3 cm-(1/8 inch)-thick rings. Spread out the rings on a large plate or shallow pan, and pour the rum over the apple slices. Let the slices sit for 20 minutes to macerate in the rum.
Whisk the egg whites to soft peaks, and fold them gently into the batter.
Fill a high-sided skillet or wide pot with 5 centimeters (2 inches) of oil, and heat the oil to 190C (375F). In batches, dip the apple rings into the batter to coat both sides, and fry, turning once, until the apple fritters are golden and crisp, about 3 minutes. Drain on paper towels, sprinkle icing sugar on top, and serve warm.