Preheat the oven to 350°F. Spray a 12x17-inch jelly roll pan with nonstick cooking spray.

In a medium bowl, whisk together the flour, baking soda, cinnamon, and salt. Set aside.

In a large mixing bowl, beat the pumpkin, sugar, and oil until smooth. Add the eggs and mix until fully combined.

Gradually add the dry ingredients to the pumpkin mixture and beat until well blended.

Pour the batter into the prepared pan and spread evenly.

Bake for 20 to 25 minutes, or until a toothpick inserted in the center comes out clean.

Let the cake cool completely before frosting.

In a small bowl, stir together the milk and vanilla. Set aside.

Place the powdered sugar in a large mixing bowl.

In a saucepan over medium heat, melt the butter, stirring constantly. Once it becomes frothy and turns a light brown color, remove from heat immediately.

Add the milk and vanilla mixture to the powdered sugar. Then pour in the browned butter.

Beat with an electric mixer until smooth and well combined.

Spread the frosting evenly over the cooled cake right away, before it begins to set.