Cardamom, Brown Butter Carrot Cake with Espresso Frosting

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Spiced Carrot Cake:

2 sticks (1 cup) unsalted butter, cut into pieces, plus more for the pan

3 cups gluten-free flour, such as Cup4Cup, plus more for the pan

3 teaspoons baking powder

1 teaspoon baking soda

1 teaspoon ground cardamom

1 teaspoon cinnamon

1/2 teaspoon ground cloves

1 teaspoon kosher salt

1/4 cup olive oil

1/4 cup vegetable oil

2 teaspoons pure vanilla extract

6 large eggs

1 1/2 cups granulated sugar

1 cup light-brown sugar

4 cups shredded carrots (about 6 medium)

Espresso Frosting:

2 tablespoons espresso powder

1 pound cream cheese, at room temperature

2 sticks (1 cup) unsalted butter, at room temperature

2 cups confectioners' sugar, sifted

2 teaspoons ground cardamom

1/2 cup candied walnuts, crushed, for garnish