Grease a Bundt pan thoroughly (spray or butter + flour).
In a large bowl, beat the eggs until light and frothy.
Add the honey, maple syrup, brown sugar, oil, and vanilla. Whisk until smooth and fully combined.
In another bowl, sift or whisk together the flour, baking powder, baking soda, cinnamon, and salt.
Gradually stir the dry mixture into the wet mixture until just combined — don’t overmix. Fold in the shredded Pink Lady apples and any juice from shredding.
Pour the batter into the prepared Bundt pan. Smooth the top and tap the pan to remove air bubbles.
Bake 75–90 minutes, or until a toothpick inserted in the thickest part comes out clean.
Cool the cake in the pan for 10–15 minutes, then invert onto a rack or plate to cool completely.
Whisk together powdered sugar, vanilla, and ½ tsp water in a small bowl. Adjust the consistency by adding more water a few drops at a time until it's drizzleable.
Drizzle over the cooled cake and let it set before slicing.