Preheat oven to 350ºF with racks in upper and lower thirds. Line 2 12-cup muffin tins with 20 paper liners. Drain pineapple, pressing on fruit. Reserve pineapple and 1/4 cup juice separately.
Whisk flours, baking soda, cinnamon, ginger, salt and nutmeg. In a large bowl, whisk eggs, oil, buttermilk, honey, brown sugar and vanilla. Stir in flour mixture. Mix in carrots and pineapple.
Fill liners almost to top. Bake, switching tins halfway through, until tops spring back when pressed, 14 to 16 minutes. Let cool slightly in tins, then transfer to wire racks to cool completely.
Whisk cream cheese, reserved juice and confectioners' sugar until smooth. Spread 1/2 Tbsp. glaze on each cupcake and serve. Refrigerate leftovers.
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