Preheat the oven to 350°F (175°C) and coat a standard bundt pan with nonstick spray or butter.
Add the butter to a saucepan over medium heat. Let it melt, then keep stirring as it foams and crackles. After about 4–5 minutes the milk solids will turn golden brown and the butter will smell nutty. Take it off the heat right away so it doesn’t burn.
1 cup (227 g) salted butter
In a large mixing bowl, whisk together the browned butter and brown sugar with an electric hand mixer.
1 cup (200 g) light brown sugar
Add the eggs, milk, and vanilla, and whisk until fully combined.
3 large eggs, 1¼ cups (300 ml) whole milk, 1 tsp (5 ml) vanilla extract
Mix in the baking powder, baking soda, cinnamon, and flour until the batter is smooth.
2 tsps (8 g) baking powder, ¾ tsp (4 g) baking soda, 1 tbsp (8 g) ground cinnamon, 2 cups (250 g) all-purpose flour
Fold in the shredded carrots.
2 cups (220 g) freshly shredded carrots
Pour the batter into the prepared bundt pan. Bake for 35–40 minutes, or until the edges are crisp and a toothpick inserted in the center comes out clean.
Cool the cake in the pan for 5 minutes, then turn it out onto a wire rack to finish cooling.
Make the frosting by beating the cream cheese, confectioners’ sugar, and vanilla until smooth.
8 oz (226 g) full-fat cream cheese, 2 cups (240 g) confectioners' sugar, 1 tsp (5 ml) vanilla extract
Spread the frosting evenly over the cooled cake and sprinkle with walnuts.
½ cup (60 g) chopped walnuts