In a large skillet, melt butter over medium heat. Cook, whisking constantly with a wooden spoon, until milk solids sink to the bottom of the skillet and turn light golden brown, 3 to 4 minutes. Add apples and stir to evenly coat in butter. Cook, stirring occasionally, until apples are crisp-tender and still hold their shape, about 5 minutes. Add lemon juice, 2 tablespoons of the sugar, and a pinch of salt. Cook, stirring constantly, until sugar dissolves and apples are glazed in sugar mixture, about 2 minutes. Transfer apples to a large plate and refrigerate until cool, about 20 minutes.

Set a wire rack inside a 13- by 18-inch rimmed baking sheet; set aside. Fill a large Dutch oven with 1 ½ inches of canola oil and heat over medium-high until oil is 375ºF (190ºC).

In a large bowl, whisk flour, baking powder, apple pie spice, remaining ½ cup sugar, and 1 teaspoon salt to combine; set aside. In a medium bowl, whisk eggs, milk, sour cream, and vanilla to combine. Add sour cream mixture and cooked apples to dry ingredients, and, using a flexible spatula, fold together until a thick batter forms.

Working in batches of 3, carefully drop about ½ cup of batter into hot oil and, using the back of a spoon, immediately press fritter until fritter is about 4-inches in diameter. Fry, adjusting heat as needed to maintain temperature, and use a spider skimmer or slotted spoon to flip fritters halfway through. Cook until fritters are browned, puffed, and cooked through, about 5 minutes. Transfer finished fritters to prepared wire rack and repeat with remaining fritters.

In a medium bowl, whisk confectioners’ sugar, apple cider, and salt until smooth. Working with one fritter at a time, dip top of fritter into glaze, allowing excess glaze to drip off. Return fritter to wire rack, glaze side up. Repeat with remaining fritters. Serve warm or at room temperature.