1. Place a rack in the center of the oven and preheat to 350°F. Lightly grease a half sheet pan (17.25×12.25 inches with 1-inch rim) with butter or shortening and dust with flour. Set aside.

2. In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking soda, cinnamon, nutmeg, and salt.

3. In a small saucepan, melt the butter with the apple cider over medium heat until steaming and just starting to bubble. Carefully pour the hot mixture over the dry ingredients and whisk until smooth and glossy.

4. Allow the batter to cool slightly. Then whisk in the eggs, vanilla extract, and sour cream until smooth. Pour the batter into the prepared sheet pan and spread evenly with an offset spatula.

5. In a small bowl, toss the diced apples with sugar, cornstarch, and cinnamon. Scatter the apples evenly over the batter and gently swirl them in with an offset spatula.

6. Bake for 18-22 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs.

7. While the cake bakes, melt butter and apple cider together in a saucepan. Whisk in powdered sugar, sour cream, and cinnamon until smooth and pourable.

8. As soon as the cake comes out of the oven, pour the warm glaze evenly over the hot cake. Use an offset spatula to spread it to the edges.

9. Let the cake cool until just warm before slicing into squares. Serve straight from the pan.