Preheat oven to 250°. Place a wire baking rack in a sheet pan and set in oven. Your waffles will rest here as you finish cooking each one.
To make brown butter, melt 4 tablespoons butter in a pan over medium heat. Swirl the pan continuously until the butter turns golden brown and smells nutty, then remove it from the heat. Immediately add 1 tablespoon of cold butter and allow it to melt. This will stop the brown butter from burning. Set aside to cool.
Peel your apple. Grate it on the large holes of your box grater. If you don't have a grater, peel and then chop your apples into a very small dice.
Combine flour, cornstarch, brown sugar, baking powder, baking soda, and salt in a large bowl and set aside.
In a large bowl, whisk milk, yogurt, eggs, and vanilla.
Add flour mixture to the wet ingredients to the and stir until halfway combined. Drizzle in butter while continuing to mix. Fold in grated apple. Allow batter to rest for 10 minutes while you heat up your waffle maker to your preferred setting.
Pour about ½ cup of batter onto preheated waffle maker, or the amount suggested by your waffle maker directions. Cook to manufacturer instructions, or about 4-5 minutes.
Transfer the cooked waffles to the wire rack and keep warm in the preheated oven as you cook the rest. Repeat to cook the remaining waffles.
Serve with a sprinkle of cinnamon sugar, a pat of butter, and a drizzle of warm maple syrup. Garnish with fresh apple slices.