Preheat oven to 350 degrees. Gather ingredients so that you have everything close at hand on the counter or table. Grease and flour a 9 or 10-cup Bundt cake pan or spray it with Baker's Spray.
Prepare the Cake Batter
In a large mixing bowl, combine the French vanilla cake mix, instant French vanilla pudding, Irish Cream Liqueur, half-and-half cream, large eggs, and vegetable oil. Mix together well on medium-high speed for 2-3 minutes.
With a rubber spatula, fold in the miniature semi-sweet chocolate chips.
Pour the batter into the prepared Bundt cake pan. Lightly tap the pan on the counter once to break any air bubbles in the batter.
Bake in preheated oven on middle to lower rack for 45-50 minutes until cake tests done with a toothpick.
Make the Glaze
In a small bowl, whisk together the Irish Cream Liqueur, half-and-half cream, and powdered sugar. Mix well until smooth and creamy.
Poke the bottom of the cake with a fork so there are many holes for the glaze to seep into.
Gradually pour the glaze over the bottom of the cake, allowing time for the glaze to seep into the holes and along the sides of the pan. Continue doing so until all of the glaze has been used.
Allow to cool in the pan for at least 2 hours. Carefully, turn out onto a cake plate for serving. Serves 18-20.