Step 1: Reduce the Apple Cider

1. Reduce the Cider: Begin by pouring the apple cider into a small saucepan. Bring it to a boil over medium-high heat, and then reduce the heat to low. Allow it to simmer for about 10-15 minutes, or until the cider has reduced to about 1/4 cup. This concentrates the apple flavor and removes some of the water content. Set it aside to cool.

Step 2: Prepare the Donut Batter

1. Preheat the Oven: Preheat your oven to 350°F (175°C). Grease a donut pan with non-stick spray or brush it with melted butter to ensure the donuts don’t stick.
2. Mix the Dry Ingredients: In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt. Set this bowl aside.
3. Cream the Butter and Sugar: In a separate mixing bowl, beat the softened butter and granulated sugar together until the mixture is light and fluffy, about 3 minutes. This creates air pockets in the batter, helping the donuts rise and become fluffy.
4. Add the Eggs and Vanilla: Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract. Mix until the batter is smooth and creamy.
5. Add the Wet and Dry Ingredients: With the mixer on low speed, gradually add the dry ingredients to the butter mixture, alternating with the milk and reduced apple cider. Start and end with the dry ingredients. Mix until just combined—be careful not to overmix, as this can lead to dense donuts.

Step 3: Fill the Donut Pan

1. Fill the Pan: Spoon the batter into the prepared donut pan, filling each cavity about 3/4 full. If you prefer, you can use a piping bag or a zip-top bag with the tip cut off to pipe the batter into the pan for a cleaner result.
2. Smooth the Batter: Gently tap the pan on the counter to settle the batter and smooth the tops with a spatula or spoon.

Step 4: Bake the Donuts

1. Bake the Donuts: Place the filled donut pan in the preheated oven and bake for 12-15 minutes, or until a toothpick inserted into the center of the donuts comes out clean. The donuts should be slightly golden around the edges and puffed up.
2. Cool the Donuts: Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.

Step 5: Coat the Donuts

1. Cinnamon Sugar Coating: While the donuts are cooling, mix the granulated sugar and cinnamon in a shallow bowl. Once the donuts are cool enough to handle, dip each donut into the cinnamon sugar mixture, coating both sides.
2. Optional Glaze: If you prefer a glaze, whisk together the powdered sugar, apple cider, and vanilla extract in a small bowl until smooth. Drizzle the glaze over the cooled donuts for an extra sweet touch.

Step 6: Serve and Enjoy

1. Serve the Donuts: Serve your baked apple cider donuts immediately, or store them in an airtight container at room temperature for up to 3 days. These donuts are perfect with a cup of hot cider, coffee, or tea, making them an ideal fall snack.