For the Cake:

1. Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line with parchment paper.
2. In a medium bowl, whisk together the flour, butterscotch pudding mix, baking powder, and salt. Set aside.
3. In a large bowl, cream the butter, brown sugar, and vegetable oil using an electric mixer on medium speed for about 3-4 minutes until light and fluffy.
4. Add vanilla extract and eggs, one at a time, mixing well after each addition.
5. Gradually add the dry ingredients, alternating with the milk, starting and ending with the dry ingredients. Mix until just combined.
6. Divide the batter evenly between the prepared cake pans and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
7. Let cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.

For the Butterscotch Frosting:

1. Beat the room temperature butter with an electric mixer until smooth and creamy.
2. Add the melted butterscotch chips and mix until fully combined.
3. Gradually add powdered sugar, one cup at a time, beating until smooth and fluffy after each addition.
4. Add salt and milk/cream, and beat until the frosting is light and spreadable.

Assembling the Cake:

1. Place one layer of the cooled cake on a serving plate.
2. Spread a generous layer of butterscotch frosting over the top.
3. Add the second cake layer and frost the top and sides with the remaining frosting.
4. Decorate the top with additional butterscotch chips.
5. Allow the cake to set before slicing and serving.