Preheat the oven to 250 degrees F. Grease a shallow 2- to 2 1/2-quart baking dish with butter.
For the pudding: In a medium saucepan, combine the milk and butter, and warm over low heat until the butter melts. In a medium bowl, whisk together the cornmeal, flour and salt. In a separate bowl, whisk a little of the milk-butter mixture with the molasses; whisk this into the cornmeal mixture. Add all of the cornmeal mixture to the saucepan and whisk until the ingredients are fully integrated. Cook for 2 minutes, stirring constantly.
Whisk the eggs in a medium bowl. Gradually whisk in some of the cornmeal mixture to temper the eggs. Pour everything back into the saucepan and gently whisk in the sugar, cinnamon, nutmeg, allspice and raisins. Empty the saucepan into the prepared baking dish and bake until the pudding looks like a slightly moist cornbread or a steamed pudding, 2 hours.
For the apples: Cut each of the apples into 8 to 10 equal-sized wedges. Melt the butter in a large skillet. Add the apples and stir to coat. Sprinkle with the brown sugar and cook, stirring with a wooden spoon from time to time, until the apples are tender and yield slightly when pierced with a knife tip. Add the lemon zest, lemon juice and ginger, and stir to blend. Keep warm while the pudding cooks.
Once the pudding is cooked, set it aside to cool. Top with the apples and serve with vanilla ice cream.