Preheat your oven to 325°F (163°C). Grease a 9x13-inch baking pan with butter or cooking spray, then dust lightly with flour and tap out the excess.
Peel, core, and dice your apples into ½-inch (1.25cm) cubes — you'll need about 4 cups (560g). Set aside.
In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking soda, cinnamon, nutmeg, cloves, and salt until fully combined with no lumps.
Make a well in the center of the dry ingredients and add the eggs, vegetable oil, and vanilla extract. Stir from the center outward until a thick, uniform batter forms with no dry streaks.
Add the diced apples and chopped nuts (if using) to the batter and fold with a sturdy spatula until evenly distributed throughout the thick batter.
Scrape the batter into the prepared pan and spread it evenly to the corners using a spatula or the back of a spoon.
Bake for 55 to 65 minutes, until a toothpick inserted in the center comes out clean or with a few moist crumbs. The top should be deep golden brown.
Transfer the pan to a cooling rack and let the cake cool in the pan for at least 20 to 30 minutes before glazing, or allow to cool completely for cleanest slices.
Whisk together the powdered sugar, 2 to 3 tablespoons of milk, and vanilla extract until smooth and pourable, then drizzle over the cooled cake and let set for 10 to 15 minutes before slicing.