Preheat the oven to 350°F (180 °C). Lightly coat a 10-inch Bundt pan with nonstick spray and dust it with flour, tapping out any excess.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger.
In the bowl of a stand mixer fitted with the paddle attachment, beat the oil, butter, and 2 1/2 cups granulated sugar on medium speed until light and fluffy, about 3 minutes. Add the eggs, 1 at a time, beating well after each addition. Use a spatula to scrape down the sides of the bowl and then gradually beat in the apple cider until incorporated.
On low speed, add the flour mixture in 3 additions, alternating with the sour cream and beginning and ending with the flour, beating just until combined after each addition. Using a spoon, gently fold in the chopped apples.
Scrape the batter into the prepared Bundt pan and use a spatula to smooth the surface. Bake the cake, rotating the pan after 30 minutes, until a toothpick inserted in the center of the cake comes out clean, 55 to 65 minutes. Let the cake cool in the Bundt pan on a wire rack for 10 minutes.
While the cake cools, in a small saucepan over low heat, combine the remaining 1/2 cup sugar and water, stirring until the sugar completely dissolves, about 5 minutes. Remove the pan from the heat.
Invert the cake onto a wire rack placed on a baking sheet. Brush the top and sides of the cake with the warm sugar syrup. Let the cake cool completely.