Follow these simple steps to create your very own Brown Butter Apple Upside Down Cake:

1. Preheat Your Oven: Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter.
2. Brown the Butter: In a medium saucepan, melt the unsalted butter over medium heat. Stir continuously until it becomes golden brown and releases a nutty aroma. Remove from heat and let cool slightly.
3. Prepare the Apples: In the same pan, add the sliced apples and brown sugar. Stir to coat and let them cook for about 5 minutes, until softened slightly.
4. Arrange Apples: Spread the apple mixture in an even layer at the bottom of your prepared cake pan.
5. Mix Dry Ingredients: In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
6. Mix Wet Ingredients: In another bowl, beat together the eggs, granulated sugar, vanilla extract, milk, and the browned butter.
7. Combine Mixtures: Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix.
8. Pour Batter: Carefully pour the batter over the arranged apples in the cake pan, smoothing out the top.
9. Bake: Place the pan in the preheated oven and bake for 45 minutes or until a toothpick inserted in the center comes out clean.
10. Cool: Once baked, remove from the oven and let the cake cool in the pan for about 10-15 minutes. Then, carefully invert it onto a serving plate.

These steps will guide you in creating the ultimate Brown Butter Apple Upside Down Cake. The process may seem lengthy, but it is straightforward and rewarding.