Prep three 8-inch cake pans with parchment paper on the bottom and greased sides. Preheat the oven to 350°F (176°C).
Combine flour, pudding mix, baking powder, and salt in a medium bowl; set aside.
Beat together butter, brown sugar, and vegetable oil in a large mixer bowl until light and fluffy (3-4 minutes). Ensure proper creaming time.
Mix in eggs and vanilla extract until fully combined and smooth. Scrape down the bowl's sides as needed for thorough incorporation.
Add half of the dry ingredients to the batter; mix until mostly combined.
Incorporate milk until well mixed (the batter may appear slightly curdled, which is normal).
Add the remaining dry ingredients, mixing until well combined and smooth. Be cautious not to overmix the batter; scrape the bowl's sides for thorough incorporation.
Evenly distribute the batter among the cake pans and bake for 22-25 minutes or until a toothpick comes out with a few crumbs.
Let the cakes cool for 2-3 minutes, then transfer them to cooling racks to cool completely.
For the butterscotch frosting, beat the butter in a large mixer bowl until smooth.
Gradually mix in the melted butterscotch chips until well combined.
Add half of the powdered sugar, salt, and half of the milk or cream, mixing until well combined.
Incorporate the remaining powdered sugar until smooth.
Adjust the frosting's consistency by adding the remaining milk or cream as needed. Set the frosting aside.
Level the cakes by removing any domes from the tops using a large serrated knife, if necessary. Place the first cake on a serving plate or a cardboard cake round.
Spread about 1 cup of frosting in an even layer on top of the cake.
Add the second cake layer on top of the frosting.
Apply another cup of frosting on the cake's top, spreading it into an even layer.
Frost the outside of the cake after adding the remaining layer. Refer to my tutorial for a smooth cake frosting if necessary.
Immediately press butterscotch chips into the cake's sides after frosting.
Use the remaining frosting to pipe shells around the cake's border.
Store the cake in an airtight container. For the best taste, consume the cake within 3-4 days.