Preheat the oven to 325°F.

To make the cake: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.

Place the flour, sugar, pudding mix, baking powder, salt, butter, and vegetable oil in a mixing bowl, and mix at medium speed until everything is thoroughly combined and the mixture is sandy looking.

Beat in the milk, then beat in the eggs one at a time. Scrape the bowl thoroughly, and beat briefly to recombine any sticky residue.
Stir in the rum and vanilla.

Spritz a 10- to 12-cup Bundt pan with cooking spray. For an extra layer of nutty flavor, sprinkle the inside of the pan with almond flour and turn the pan to coat evenly; shake out any excess. Pour the batter into the prepared pan and spread level with a spatula.

Bake the cake for 50 to 60 minutes. When done, a cake tester, long toothpick, or strand of uncooked spaghetti will come out clean when inserted into the center. Remove the cake from the oven.

Leave the cake in the pan to cool slightly while you make the syrup.

To make the syrup: In a medium-sized saucepan combine the syrup ingredients, except vanilla. Bring to a rapid boil then reduce to a simmer and cook (without stirring) for about 5 to 8 minutes, until the syrup thickens slightly. Remove from the heat and stir in the vanilla.

Use a long skewer to poke holes all over the cake. Pour about 1/4 cup of the syrup over the cake (still in the pan). Allow the syrup to soak in, then repeat again and again until all the syrup is used.

Cover the pan loosely with plastic wrap and allow the cake to sit overnight at room temperature to cool completely and soak in the syrup. When ready to serve, loosen the edges of the cake and invert onto your serving plate. If the cake won’t release, don't force it. Place it in the oven, turn the oven to 350°F, and warm for about 10 minutes, to soften the sticky syrup. (If your oven is one that preheats by making its upper element red-hot, place the cake on a lower rack and tent it with aluminum foil to protect it.) Remove the cake from the oven, and tip it onto the serving plate.

Serve with hot coffee or tea. The cake is very moist, fragrant and potent.

Wrap securely (or place under a cake cover) and store at room temperature for several days. Freeze for longer storage, up to 1 month.