Preheat the oven to 350F. Grease a 10.5x7.5” or 8x8” baking dish/pan with butter. Set aside.

Add the ½ cup (113g) of butter to a saucepan over medium-high heat. Allow to melt and brown, while stirring continuously (~5-8 minutes). As the butter continues to cook, you’ll notice that it starts to foam up across the surface (after about 2 minutes). Continue cooking, stirring with a spatula, until the milk solids begin to brown (the brown specks at the bottom of the pan) and the color starts to deepen. Once the brown butter reaches a deep golden amber color and smells nutty, remove from the heat and immediately pour into a large bowl. Set aside to cool slightly (about 15-20 minutes), enough so it doesn’t melt the sugars when added.

In a large saucepan over medium-high heat, add the butter, diced apples, brown sugar, cinnamon, apple pie spice (if using), and salt. Cook until the sugar melts and the apples start to soften, stirring occasionally (~10 minutes). It can help to steam the apples by covering the pan with a lid for a few minutes.

Once the apples are soften, have released their juices, and the mixture has become slightly thickened and gooey, remove from the heat and stir in the vanilla. Set aside to cool while you continue preparing the batter.

Prepare the cinnamon swirl by mixing together the brown sugar and cinnamon in a small bowl. Set aside.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and apple pie spice (if using). Set aside.

To the bowl with the cooled brown butter, add the brown sugar and whisk to combine.

Add the Greek yogurt (or sour cream) and whisk to combine. Then whisk in the eggs and vanilla. Finally, add the milk and whisk until well combined. If the mixture turns lumpy, that’s totally okay! Once you add the flour mixture, it will all come together nicely.

Add the dry ingredient mixture to the wet, and gently whisk to combine (the batter should be thick at this point).

Then, add half of the cooked apples to the batter (reserving the rest for topping later), and use a wooden spoon or spatula to gently fold them into the batter.

Transfer or scoop half of the batter into the prepared pan and spread into an even layer. Sprinkle the surface with half of the cinnamon swirl mixture. Then top the cinnamon swirl with the remaining half of the batter, spreading it into an even layer. Finally, finish by dispersing the remaining cooked apples over the surface of the batter and sprinkling the remaining cinnamon swirl mixture all over the top.

Bake at 350F for 50-60 minutes, or until golden and a toothpick inserted into the middle comes out clean or with moist crumbs.

Remove from the oven and let cool for 5-10 minutes.

While the cake is baking, prepare the glaze. In a medium bowl, whisk together the powdered sugar, maple syrup, milk, vanilla, and salt until smooth.

After the cake has cooled for 5-10 minutes, drizzle the glaze all over the top.

Scoop the cake directly from the pan and serve warm with vanilla ice cream for dessert, or a cup of coffee for a cozy breakfast.