Spray 12 muffin tins with nonstick spray. In a medium bowl, stir muffin mix, bran, milk, and egg until just blended. Fold in carrots, dates, and confectioners' sugar. Be careful not to over-mix; the batter should be lumpy. Divide batter equally among the muffin tins. Bake until a toothpick inserted into center of muffin comes out clean, about 20 minutes. Let cool slightly before frosting.
To make the cream cheese frosting, combine the softened cream cheese, confectioners' sugar, and carrot shavings in a medium bowl; stir until well blended.
Slice muffins in half, spread with the cream cheese frosting, and then sandwich together. Serve warm or at room temperature.