Preheat the oven to 350F. Peel and core the apples. Slice them into four even doughnut shaped sections, crosswise. Lay the apples on a parchment paper lined baking sheet. Dot them with butter and sprinkle with sugar. Bake until the apples are brown and tender but not completely done. Let them cool to room temperature. While the apples are baking, prepare the batter to fry them. Separate the eggs, reserving the whites. Whisk 3 egg yolks (discard the 4th one or use for something else) with the salt, butter and cider. Add the flour and whisk until smooth. In the bowl of a stand mixer, whisk the egg whites until foamy, add the sugar slowly until you get stiff glossy peaks. Carefully fold the whites into the egg yolk batter. Note about frying: do not overcrowd your pan as it will drop the temperature of the oil and you will have a soggy oily beignet instead of a crispy one. To test if the oil is ready, dip the end of a wooden spoon or dowel in the oil and if you see bubbles at the base touching the oil, it is ready. Heat one cup of oil in a frying pan to 325F. While it is heating up to temperature, mix the last measurement of sugar with the cinnamon in a plate and keep it close as you will dip the beignets in this once they are fried and cooled a bit. Dip each roasted apple slice in the batter, coating both sides and gently lay them down in the oil. Cook 4-6 apple slices depend on the size of your pan, until they start to brown around the edges ( I used an 8inch cast iron one and 4 slices at a time). Using a slotted spoon or spatula, flip the apple over and cook until golden brown. Drain them on paper towels for a minute and dredge them in the cinnamon sugar. Serve as soon as possible or reheat briefly in a pan the day after (if they last that long).