Begin by pouring 1½ cups of fresh apple cider into a wide saucepan. Heat over medium-high heat, stirring occasionally until the cider reduces by half, which should take about 10–15 minutes. You will know it's done when it measures about ¾ cup and thickens slightly, concentrating its flavor.

Once the cider is reduced, remove it from the heat and stir in 4 tablespoons of butter until melted. Let this mixture cool for about 5 minutes.

In a large mixing bowl, whisk together ⅓ cup granulated sugar, ½ cup brown sugar, ⅓ cup light olive oil, and ¼ cup sour cream until smooth. Add in 1 teaspoon of cinnamon, 1½ teaspoons of baking powder, ¼ teaspoon of baking soda, and ½ teaspoon of salt.

Gradually pour the cooled cider-butter mixture into the bowl of wet ingredients while whisking gently until fully combined.

Sift 1¾ cups of all-purpose flour into the wet mixture and gently fold with a spatula until just combined.

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.

Place the baking dish in the center of the preheated oven and bake for about 22-25 minutes. Check for doneness by inserting a toothpick into the center; it should come out clean.

After baking, let your Apple Cider Donut Cake cool in the dish for about 5 minutes. Then, brush the top with melted butter and sprinkle ¼ cup of granulated sugar mixed with a pinch of cinnamon on top.