Place 3/4 cup apple cider in a saucepan and turn heat to medium. Bring to a boil and then lower to a very high simmer until the cider reduces to 1/4 cup. This should take around 10 minutes
Place sliced apples in a glass bowl, cover with filtered water and squeeze the juice of one lemon into the water. Let apples soak for 5 minutes. Remove from water and lay slices on a paper towel. Pat dry and set aside
Place butter and sugar in a mixer and mix until creamy
Add eggs and beat until just mixed
Add flour, baking powder, baking soda, salt and half & half and beat until just mixed
Preheat oven to 350 degrees F
Use a spatula to transfer the cake batter to the 9 x 9 pan and stick each apple slice into the batter. In a small bowl mix the cinnamon and sugar and sprinkle it over the apples
Bake for 40 minutes. Test at that point and if they aren't done, place in there for 5 more minutes. Place on a wire rack when done and let cool for 15 minutes before adding the glaze
As the cake is baking, reduce 3/4 cup of apple cider to 2 tablespoons. (Follow the directions above)
To make the glaze
Add confectioner's sugar and reduced apple cider and mix with a whisk. It will be thick so add 2 tablespoons half & half and whisk until creamy
Spoon glaze into a sandwich baggie and cut the corner off of it. Drizzle glaze over the cake and let set
Cut a piece
I actually don't mind when apples turn brownish, but for this recipe I place the sliced apples in lemon water to curb the browning.
To reduce the apple cider, you heat it to a boil, then turn down the heat to a high simmer until it reduces to the correct amount - 1/4 cup for the cake and 2 tablespoons for the glaze.
I always reduce the apple cider for the batter and glaze separately because I can control the amounts easily.
I've used different apples in this cake but prefer Granny Smith because they hold up really well and don't get mushy.
I use a sandwich bag for piping the glaze on this cake but if you have a pastry bag, feel free to use it.