Heat the apple cider: Heat the apple cider to roughly 100-105°F.
Activate the yeast: In a small bowl, combine the heated apple cider, 2 tbsp of sugar, and the active dry yeast. Let it sit for 5–10 minutes until it becomes foamy.
Mix the wet ingredients: In a large mixing bowl, Add the sourdough discard, melted butter, egg, and vanilla extract to the yeast mixture. Stir until well combined.
Combine dry ingredients: In a separate bowl, whisk together the flour, 1 tsp of cinnamon, allspice, nutmeg, and salt. Gradually add the dry ingredients to the wet mixture, stirring until a soft dough forms.
Knead and rise: Turn the dough out onto a lightly floured surface and knead for 5–7 minutes, or until smooth and elastic. Place the dough in a lightly greased bowl, cover, and let rise in a warm spot for about 1.5 hours, or until doubled in size.
Shape the donuts: Roll the dough out to about ½-inch thickness on a floured surface. Use a donut cutter (or a large glass and a small bottle cap) to cut out the donuts and holes. Place them on a parchment-lined baking sheet, cover lightly, and let rise for another 30 minutes.
Fry the donuts: Heat about 2 inches of oil in a deep, heavy-bottomed dutch oven to 350°F (175°C). Fry the donuts in batches for 1–2 minutes per side, or until golden brown. Use a slotted spoon to transfer the donuts from the hot oil to a wire rack.
Coat the donuts: Mix the remaining ½ cup sugar and 1 tsp cinnamon in a shallow dish. While the donuts are still warm, roll them in the cinnamon sugar mixture to coat evenly.
Serve and enjoy: Enjoy your sourdough discard apple cider donuts fresh, paired with a cup of coffee, tea or hot apple cider!