Arrange a rack in the middle of the oven and heat the oven to 350ºF. Coat a 9x13-inch baking pan, preferably metal, with cooking spray. Line the bottom and two long sides of the pan with a sheet of parchment paper that extends a few inches over the sides to form a sling.

Peel and core 4 medium apples. Dice 3 of the apples (about 4 ⅓ cups). Grate the remaining apple on the large holes of a box grater (about 1 cup).

Place 2 ¼ cups all-purpose flour, 2 teaspoons ground cinnamon, 2 teaspoons baking powder, ¾ teaspoon baking soda, ½ teaspoon ground nutmeg, ½ teaspoon kosher salt, ¼ teaspoon ground ginger, and ¼ teaspoon ground allspice in a medium bowl and whisk to combine.

Place ¾ cup vegetable oil, ¾ cup granulated sugar, ½ cup packed light brown sugar, ½ cup full-fat Greek yogurt, 4 large eggs, and 1 teaspoon vanilla extract in a large bowl and whisk to combine. Add the flour ingredients in 2 increments, stirring with a flexible spatula until fully incorporated.

Add the grated apple and about ⅔ of the diced apples. Fold into the batter until combined. Transfer the batter into the baking pan and smooth out the top. Sprinkle with the remaining diced apples.

Bake until the top is golden-brown, springs back slightly when gently pressed, and a toothpick inserted into the center comes out clean, 45 to 50 minutes. Let cool for 20 minutes in the pan. Grasping the excess parchment, lift the cake slab out the pan and place on a wire rack. Let cool completely, about 1 ½ hours.

Place ⅔ cup powdered sugar and 1 tablespoon milk in a small bowl and whisk until smooth. Drizzle over the top of the apple cake. Serve immediately or let sit for 10 minutes for the glaze to set first.