1-Preheat and Prepare: Begin by preheating your oven to 350°F (175°C) and greasing and lining an 8×8-inch cake pan. This sets the stage for even baking and easy removal later. Brown the butter in a saucepan over medium-low heat until the milk solids caramelize and it gives off a nutty aroma; stir occasionally to avoid burning.

2-Mix the Dry Ingredients: In a large bowl, whisk together 1 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, and 1/2 teaspoon kosher salt. This step ensures your dry mix is even and ready to blend smoothly. Set it aside while you work on the wet ingredients.

3-Combine Wet Ingredients: In another bowl, beat the browned butter with 1 cup granulated sugar, 2 tablespoons neutral oil, and the scraped seeds from 1 vanilla bean (or 2 teaspoons vanilla extract) for about 1 minute. Add 2 large eggs and mix until fully combined, creating a rich base for your batter.

4-Build the Batter: Alternate adding the dry ingredients and 1/2 cup whole milk to the wet mixture, stirring gently until everything is incorporated and the batter looks smooth. Be sure to scrape the bowl to eliminate any flour pockets, which helps avoid uneven spots in your cake.

5-Bake and Cool: Pour the batter into your prepared pan and bake for 23 to 25 minutes, or until a skewer inserted in the center comes out clean. Let the cake cool in the pan for 5 to 7 minutes, then invert it onto a cooling rack and let it cool completely for about 1 hour.

6-Make the Frosting and Finish: For the frosting, beat 3/4 cup unsalted butter until smooth, then sift in 2 cups powdered sugar and add 2 tablespoons maple syrup, 1 tablespoon heavy cream, and a pinch of kosher salt. Beat for 2 minutes until it’s light and fluffy. Spread it over the cooled cake, add decorative swoops if you like, and top with cookies or sprinkles before slicing and serving.