Preheat the oven to 325 degrees F. Grease a 9x5 inch loaf pan (I use baking spray with flour).
In a medium sized bowl, whisk together the flour, pudding mix, baking powder and salt. In a liquid measuring cup, combine the half & half and vanilla extract.
In a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium high speed for several minutes until light and fluffy. Scrape down the sides of the bowl with a spatula.
Turn the speed down to medium low and add the eggs, one at a time, allowing each egg to fully incorporate and scraping down the sides of the bowl between each egg. The mixture will become thin and look slightly broken, which is fine.
Working swiftly, alternate between adding the dry and wet ingredients, starting and ending with the dry. The less the batter is worked at this stage, the better. You do not need to let the ingredients incorporate fully before alternating.
Divide approximately half of the batter into a second bowl and stir in the melted chocolate until evenly combined.
You have two options at this point. To recreate my grandma's cake, spread the pale batter evenly into the bottom of the pan and top evenly with the chocolate batter. For a marble cake, alternate between scooping the two batters into the loaf pan. Once the batter has all been distributed, use an offset spatula or butter knife to draw several zigzags through the batter. Gently level off the top of the cake with a spatula.
Place the loaf pan on a baking sheet and carefully place in the oven. Bake for 80 to 90 minutes, or until a toothpick comes out clean. Do not over-bake or the cake will be dry. Allow to cool in the pan for 20 minutes and then move to a cooling rack to finish cooling.
Notes
I melt the bittersweet chocolate by breaking it into small pieces, placing it in a microwave safe bowl and nuking it for 30 second increments, stirring each time, until the chocolate is smooth.