Combine the cider, ginger beer, butter, sugar, and salt in a large saucepan and bring to a rolling boil over medium-high heat. Remove from the heat and add the flour all at once, stirring hard with a wooden spoon until all the flour is incorporated. Return the pan to the heat and cook, stirring, for about 2 more minutes, to evaporate some of the moisture.
Remove the dough from the heat. Beat in the eggs one at a time, pausing after 3 eggs to check the consistency. The dough should be smooth and glossy and run slowly off the spoon when you lift it. If you reach this stage after 3 or 4 eggs, do not continue adding eggs to the dough.
Line a baking sheet with parchment paper (cut into small 4X4 inch squares. Fit a pastry/frosting bag with a large star tip, and spoon the dough into the bag. Pipe the dough into wreaths about 2-3 inches in diameter. Freeze the doughnuts on the tray for at least 20-25 minutes.
Make the glaze by whisking together the powdered sugar, milk, honey and almond extract until smooth.
To fry the doughnuts, heat the 1 1/2 inches of vegetable oil in a wide frying pan over medium heat. Heat the oil to 325°F (If you don't have a thermometer, you can test the temp of the oil by inserting the end of your wooden spoon into the oil. When it begins to bubble, it's ready!). Working in batches, add the frozen doughnuts to the hot oil and fry until they float to the top and are golden brown all over, about 2-3 minutes. You may need to carefully flip the doughnuts over once while they are frying for even cooking. Use a slotted metal spoon or skimmer to remove the doughnuts from the oil and drain on a paper bag. Once cool enough to touch, dip the warm doughnuts into the glaze and let cool on a cooling rack. Serve immediately.