Step 1
Place butter in a light-colored saucepan over medium heat. Cook swirling the pan constantly until butter is bubbling smells nutty and browned bits begin to form on the bottom of the pan 5 to 10 minutes. Immediately remove from heat and pour butter into a heat-safe bowl. Allow brown butter to cool to room temperature about 15 minutes.
Step 2
Preheat the oven to 325 degrees F (165 degrees C). Grease a 12x16-inch pan and line with parchment paper.
Step 3
Whisk together flour baking soda baking powder cinnamon allspice nutmeg and salt in a bowl.
Step 4
Beat cooled brown butter and brown sugar in a large bowl with an electric mixer on medium speed until well combined. Beat in eggs one at a time mixing well after each addition until mixture is light and fluffy. Mix in vanilla. Pour in 1/2 of the flour mixture and mix until just combined. Add in remaining flour mixture and mix until just combined.
Step 5
Fold in shredded carrots walnuts and raisins. Pour batter into the prepared pan and smooth out the top with a spatula.
Step 6
Bake in the preheated oven until cake is golden and a toothpick inserted into the center of it comes out clean 23 to 27 minutes. Transfer onto a wire rack and cool completely about 30 minutes.
Step 7
While cake is cooling repeat step 1 to brown butter for the frosting. Let cool to room temperature about 15 minutes.
Step 8
Beat cream cheese in a large bowl with an electric mixer on medium-high speed until completely smooth. Add in cooled brown butter and mix until thoroughly combined. Mix in powdered sugar 1 cup at a time beating well after each addition. Mix in vanilla and salt. Beat frosting at medium-high speed until completely smooth 1 to 2 minutes.
Step 9
Spread frosting over the cooled cake. Chill cake until ready to serve.