This batter is very stiff until you fold in the carrot. Its moisture smooths out the mixture.
Beat first 4 ingredients at medium speed with an electric mixer 2 to 3 minutes. Combine flour and next 3 ingredients; gradually add to sugar mixture, beating at low speed until blended. Fold in carrot and pecans. Spoon into greased and floured 8-ounce ramekins or 6-ounce custard cups, filling two-thirds full.
Bake at 325° for 25 to 30 minutes. Cool on wire racks 10 minutes. Invert onto serving dishes; serve warm with Madeira Syrup and ice cream. Garnish, if desired.
Note: Cakes may be baked in large (3-inch) muffin pans.