Peel and cut the apples into small cubes. I like using my apple corer and slicer to make this process easy and quick.
Preheat an oven to 180c (350f) and prepare a 9x9 inch cake pan with parchment paper.
In a large mixing bowl, add the eggs, cooled melted butter, cinnamon, yogurt, granulated sugar, milk, kosher salt, and vanilla extract, and mix well with a whisk.
Add the flour, baking powder, and baking soda, and mix with a whisk until almost combined.
Add the chopped apples and mix until just combined and there are no lumps of flour visible. Do not overmix.
Into a small mixing bowl, add melted butter, cinnamon, and sugar, and mix with a spoon until well combined.
Pour the cake batter into a prepared 9 by 9 inch pan with parchment paper and smooth it out with a spatula. Spoon the cinnamon topping on top of the cake and make swirls using a butter knife.
Bake in a 180c (350f) preheated oven for 45-50 minutes (depending on your oven) or until a toothpick comes out clean.
In a small mixing bowl, add the powdered sugar, milk, and vanilla. Mix with a spoon until the mixture is well combined and until the glaze is smooth and silky.
Top the cake with as much glaze as you would like, and serve warm next to a cup of coffee or hot tea. Enjoy!
Notes
Use room temperature ingredients. It is important that you use room-temperature ingredients like eggs and milk. This step ensures that your mixture mixes into a homogenous mixture and bakes perfectly. you don’t want to place cold batter into the oven.
To make this process easy, quick, and clean, use an apple peeler and corer. Here is the one I use all the time.
Line your baking pan with parchment paper! This step helps the cake to bake evenly, and it makes sure that your cake will release easily from the pan.
Don’t overmix the batter, you don’t want to develop the gluten in the flour. This step ensures you have moist cake and not dense and dry cake.
Measure your flour correctly! When measuring your flour, avoid scooping it with a measuring cup. Instead, stir the flour with a spoon to create as many air pockets as possible, and spoon it into your measuring cup. Finally, level it with the back of a knife.
Scrape down the sides and the bottom of the bowl frequently to ensure that you have a homogeneous mixture that has unmixed parts of the mixture.
Don't overbake. Check the cake 5-10 minutes before the recommended baking time. Insert a toothpick into the center; if it comes out with a few moist crumbs, the cake is done.
Be patient! It’s extremely tempting to eat this cake as soon as it's ready. Allow it to cool to room temperature before eating. This step prevents the cake from falling apart.