Preheat oven to 375°F (190°C). Lightly grease a doughnut pan with cooking spray.

In a medium bowl, whisk together the flour, cinnamon, nutmeg, baking powder, and baking soda. Set aside.

In a large bowl, cream together the softened butter, light brown sugar, and salt until smooth.

Add the egg, vanilla extract, and yogurt. Beat until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.

Using a spatula, gently fold in the crushed pineapple and shredded carrots.

Spoon the batter into a piping bag or a ziploc bag with the corner snipped off. Pipe the batter into the prepared doughnut cavities, filling each about two-thirds full.

Bake for 10 minutes, or until a toothpick inserted into the center comes out clean.

Let the doughnuts cool in the pan for 10 minutes before inverting them onto a wire rack to cool completely.

In a medium bowl, cream together the softened butter and cream cheese until smooth and creamy.

Add the pineapple juice and powdered sugar. Beat until the frosting is smooth and well combined.

Place chopped walnuts in a dry skillet over medium heat. Cook, stirring frequently, for 3-5 minutes, or until fragrant and lightly toasted.

Once the doughnuts have cooled, frost the tops with the pineapple cream cheese frosting and sprinkle with toasted walnuts.