Preheat oven to 400 degrees F (200 degrees C).
Grease and flour a 9-inch cake pan.
In a large bowl, combine 1 cup white sugar, 1 egg, and 1 tablespoon butter.
Beat with an electric mixer until creamy.
Add 1 tablespoon apricot jam, 1 tablespoon white vinegar, 2 teaspoons ground ginger, and 1 teaspoon baking soda to the mixture.
Gradually add 1 cup milk and 1 cup purpose flour to the mixture.
Beat until the batter is smooth.
Pour the batter into the prepared cake pan.
Bake in the preheated oven for about 35 minutes, or until a toothpick inserted into the center comes out clean.
In a saucepan, combine 1 cup milk, 1/2 cup butter, 1/2 cup white sugar, and 1/4 cup water.
Heat the mixture over medium heat for 5 minutes before the pudding is done baking.
Bring the sauce to a boil and stir until smooth.
Pour the hot sauce over the baked pudding and let it sink in.