Preheat oven to 350°F. Grease and flour a light-colored Bundt pan or spray it with baking spray with flour.
Whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a bowl.
In a separate bowl, mix brown sugar, granulated sugar, oil, eggs, vanilla, and Greek yogurt until smooth.
Stir in shredded carrots and well-drained crushed pineapple.
Fold in the dry ingredients until just combined. If using walnuts, stir them in last.
Pour the batter into the prepared Bundt pan and smooth the top.
Bake for 50-60 minutes at 350°F, checking at 50 minutes with a toothpick. If it browns too quickly, loosely tent with foil at 30 minutes.
Cool in the pan for 15-20 minutes, then carefully invert onto a wire rack to cool completely.
Cream Cheese Drizzle:
Beat cream cheese and butter together until smooth.
Mix in powdered sugar and vanilla.
Add milk or cream 1 tablespoon at a time until the frosting is thin enough to drizzle.
Drizzle over the cooled Bundt cake before slicing.