Cut several parchment papers into squares about 8x8cm and set aside.
In a medium sized saucepan, place the butter, sugar, water, apple cider and salt and bring to a boil over medium heat. Once it starts to boil remove from the heat. Add the flour all at once, and mix well with a wooden spoon until the flour is combined in the wet mixture.
Return the saucepan back on the stove, on medium heat and let it cook while constantly stirring for 2 minutes. Do not move away from this process!
Transfer the cooked dough to a large bowl or to your mixer, let it cool for a couple of minutes. Once slightly cooled, start adding the eggs one at a time, making sure that each egg is fully incorporated in the dough before adding another. If the dough starts to divide after adding the egg, no worries, it's normal, just keep beating.
Fill a large pot with vegetable oil, pour enough oil so that the crullers have enough space to cook in, about 7 cm. Heat the oil to about 170°C; you want the oil to be hot enough so that you reduce the cooking time avoiding that they get soggy, but at the same time you don't want the oil too hot that it burns the outside and leaves the inside raw.
For the glaze, in a small bowl, whisk together the icing sugar with the apple cider. Add an extra tbsp until you've achieved your desired consistency.
Place the dough in a piping bag, fitted with an open star nozzle. Pipe out circles on the previously cut parchment papers. Drop the cruller with the parchment paper facing up in the oil. Once it's starting to cook remove the parchment paper and let the cruller continue to cook for about 2 minutes on each side, until they are nicely golden in colour.
Drain the crullers from excess oil on some paper towels, dip them into the glaze and place them on a cooling rack.
Serve immediately and enjoy!