Banana Bread Donuts with Cream Cheese Frosting

For the banana bread donuts:

• 1 cup + 2 tablespoons all-purpose baking flour
• 1/2 cup dark brown sugar
• 1/2 teaspoon salt
• 1/2 teaspoon cinnamon
• 1/4 teaspoon ground nutmeg
• 1 teaspoon baking powder
• 1/2 cup very ripe bananas, mashed
• 2 1/2 tablespoons unsalted butter, melted
• 1 large egg, at room temperature

For the cream cheese frosting:

• 3 ounces cream cheese, very soft
• 3 tablespoons unsalted butter, very soft
• 1 teaspoon pure vanilla extract
• 1 and 1/2 cups confectioners' sugar, sifted
• 1-2 tablespoons milk
• 1/2 cup walnuts, chopped, for decorating