Creating your Brown Butter Caramel Cake can be straightforward if you follow these steps:

1. Brown the Butter: In a saucepan over medium heat, melt the unsalted butter. Continue cooking, stirring frequently, until it turns a nutty brown color and smells fragrant. Remove from heat and let it cool slightly.

2. Preheat the Oven: Preheat your oven to 350°F (175°C) and grease and flour a 9×13-inch cake pan.

3. Mix Dry Ingredients: In a bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.

4. Combine Sugars: In another large bowl, combine granulated sugar, brown sugar, and the browned butter. Mix until well combined.

5. Add Eggs and Vanilla: To the sugar mixture, add the eggs one at a time, mixing after each addition. Then add the vanilla extract.

6. Incorporate Dry Ingredients and Milk: Gradually add the dry ingredients to the butter mixture, alternating with the whole milk, starting and ending with dry ingredients. Mix until just combined.

7. Pour into Pan: Pour the batter into the prepared cake pan, smoothing the top with a spatula.

8. Bake: Place the cake in the preheated oven and bake for 40-45 minutes or until a toothpick inserted in the center comes out clean.

9. Cool the Cake: Once done, remove the cake from the oven and let it cool in the pan for about 15-20 minutes. Then, transfer it to a wire rack to cool completely.

10. Drizzle Caramel Sauce: After the cake has cooled, generously drizzle caramel sauce over the top, allowing it to soak into the cake slightly.