Preheat your oven to 350°F (175°C) and allow it to fully come to temperature. Grease a 9x13-inch baking pan with butter or non-stick spray, then line the bottom with parchment paper if desired for easy removal.
In a large bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, cloves, and nutmeg for 30 seconds until evenly combined. Sift if your flour tends to clump, then set aside.
In a second large bowl, beat the softened butter, granulated sugar, and brown sugar together with a hand mixer on medium speed for 2 to 3 minutes until light, pale, and fluffy.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract. Scrape down the sides of the bowl with a rubber spatula.
Add the unsweetened applesauce and stir on low speed until fully combined. The batter may look slightly curdled — this is normal and will resolve once the dry ingredients are added.
Add the dry ingredients and milk in three alternating additions — one-third flour, half the milk, one-third flour, remaining milk, final flour — stirring gently after each addition until just combined. Do not overmix.
If using raisins or chopped nuts, gently fold them into the batter with a rubber spatula until evenly distributed.
Pour the batter into the prepared pan, smooth the top, and bake on the center rack for 45 to 55 minutes, until a toothpick inserted into the center comes out clean. Tent loosely with foil if the top browns too quickly.
Remove the pan from the oven and place it on a wire cooling rack. Cool in the pan for at least 15 to 20 minutes before slicing, or allow to cool fully (about 1 hour) before glazing.
Whisk together the powdered sugar, milk or cream, and cinnamon in a small bowl until smooth, adjusting consistency as needed. Drizzle over the fully cooled cake and allow to set for 10 minutes before slicing.