In a heavy saucepan stir together milk and cornmeal and bring to a simmer, stirring. Stir in molasses, ginger, cinnamon, and a pinch salt and simmer mixture, stirring, 30 minutes, or until very thick. Add butter, stirring until melted. Remove pan from heat and cool pudding 20 minutes, covered.
In a saucepan simmer cider, brown sugar, water, and lemon juice, stirring occasionally, until sugar is dissolved. Add fruits and simmer 5 minutes more, or until fruits are softened and plumped up.
Put a spoonful of pudding in each of 8 shallow bowls or soup plates using a 2-ounce (1/4 cup) ice-cream scoop and top with some compote.
