In a medium saucepan over medium heat, melt the butter, swirling the pan occasionally. Once the butter starts to foam, keep stirring gently. The butter will develop a nutty aroma and light brown specks will form at the bottom of the pan. Keep stirring to prevent burning.

Once the butter turns a deep golden brown and smells nutty, remove it from the heat immediately. Pour it into a heatproof bowl, scraping in all the browned bits. Chill in the refrigerator for 1–2 hours, until firm but still soft.

Remove the butter from the refrigerator and let it sit at room temperature for about 15 minutes before using.

Preheat the oven to 350°F. Grease two 9×5-inch loaf pans with nonstick spray and line with parchment paper. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, cream the browned butter and sugar until light and fluffy, about 2–3 minutes.

Add eggs one at a time, mixing well after each addition. Add the vanilla extract and mix to combine.

Gradually add the flour and milk, alternating between the two, starting and ending with the flour. Mix until just combined. Do not overmix.

Divide the batter evenly between the prepared loaf pans. Bake for 60–65 minutes, or until a toothpick inserted into the center comes out clean or with a few crumbs attached.

Let the cakes cool in the pans for 10 minutes before transferring to a wire rack to cool completely.

Drizzle with extra browned butter before serving, if desired.