Begin by pouring 2 cups of fresh apple cider into a wide, shallow pan. Heat it over medium-high heat, simmering until it reduces by half, about 10-15 minutes.

Remove the cider from heat and let it cool slightly. In a mixing bowl, melt 4 tablespoons of unsalted butter and whisk in the warm, reduced cider, ¾ cup of granulated sugar, ½ cup of brown sugar, ½ cup of sour cream, and ½ cup of light olive oil.

Add 1 teaspoon of baking powder, ½ teaspoon of baking soda, 1 teaspoon of ground cinnamon, and ½ teaspoon of allspice to the wet mixture. Mix these dry ingredients into the wet mixture, being careful not to over-mix.

Gradually sift in 2 cups of all-purpose flour into the mixture and fold it in gently. Ensure no streaks of flour remain, but do not overwork the batter.

Preheat your oven to 350°F (175°C), and line an 8-inch square baking dish with parchment paper. Pour the batter into the prepared dish, smoothing the top.

Bake for 22-30 minutes, until golden brown and a toothpick inserted into the center comes out clean.

Brush the warm surface with 2 tablespoons of melted butter and immediately sprinkle a generous layer of cinnamon sugar over the top.

Allow the cake to cool in the dish for about 10 minutes before removing it using the parchment paper overhang. Transfer it to a wire rack to cool completely.