In a food processor (a blender is also fine), pulse together eggs, brown sugar, oil, orange juice and vanilla until well blended. Add carrots, flours, pineapple, baking soda and cinnamon; process for 20 seconds, scraping down sides halfway through, until mixture is well combined. Spoon mixture into 18 lightly greased muffin tins or a 10-cup (2.5-L) Bundt pan.
Bake in centre of preheated oven for 20 to 25 minutes for cupcakes, or 35 to 40 minutes for cake, or until top of cupcakes or cake springs back when lightly pressed. Let cool in pan on rack. (Without icing, cupcakes or cake can be frozen, well wrapped, for up to six weeks.)
Use electric beaters to beat cream cheese with sugar until fluffy. Beat in orange juice. Spread over individual cupcakes or Bundt cake.
Per serving: 227 calories, 5 g protein, 11 g fat (3 g saturated fat), 27 g carbohydrates, 2 g fibre, 50 mg cholesterol, 285 mg sodium