Carrot Bread With Hazelnuts, Coconut and Cream Cheese Glaze

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For the Bread:

1 stick unsalted butter, melted and cooled (or 1/2 cup vegetable oil), plus more for the pan

1 1/4 cups all-purpose flour

3/4 cup granulated sugar

1 teaspoon baking powder

1 teaspoon salt

1/2 teaspoon baking soda

1/2 teaspoon ground cinnamon

1/2 teaspoon grated nutmeg

3/4 cup hazelnuts, toasted and chopped

1 cup sweetened shredded coconut

2 large eggs

1/2 cup plain yogurt or sour cream

1 teaspoon vanilla extract

1 teaspoon grated lemon zest (optional)

1 cup shredded carrots

For the Glaze:

1 cup confectioners' sugar

3 tablespoons cream cheese, softened

2 tablespoons milk

1/4 teaspoon vanilla extract