Fit a wide heavy pot with candy thermometer. Pour in oil to a depth of 2" and heat over medium-high until thermometer registers 375ºF. Meanwhile, whisk flour, 1/4 cup sugar, 3/4 tsp. cinnamon, and 1 1/4 tsp. salt in a large bowl. Add beer in a slow, steady stream, whisking until smooth. Whisk pepper, cardamom, 1/8 tsp. salt, and remaining 3/4 cup sugar and 1/4 tsp. cinnamon in a medium bowl. Working with 4-5 slices at a time, dip apples in batter, shaking off excess. Fry until golden, about 1 1/2 minutes on each side. Transfer fritters with a slotted spoon to paper towels to drain. Immediately toss in spiced-sugar mixture and serve warm.