Begin by preheating the oven to 325°F. Prepare three 8x2-inch round cake pans by greasing and flouring them. For added security, line the bottom of each pan with parchment paper.
In a microwave-safe bowl, melt the butterscotch chips with two tablespoons of vegetable oil. Microwave in 20-second intervals, stirring between each, until almost melted, then stir to dissolve any remaining bits. Allow it to cool slightly before adding it to the batter.
In a mixing bowl, whisk together the yellow cake mix, flour, and dry butterscotch pudding mix. Add the eggs, sour cream, milk, vegetable oil, vanilla extract, and the melted butterscotch. Blend on low speed until ingredients are just combined, then increase speed to medium for one minute, pausing to scrape down the sides of the bowl. Continue mixing for another minute. The batter may feel thick, but it will bake up light and airy.
Divide the batter evenly across the prepared pans (approximately 6 cups in total). Bake for 22-25 minutes or until a toothpick inserted into the center comes out clean or with just a few moist crumbs. The cake should spring back when gently pressed. Allow the cakes to cool in the pans for 5-10 minutes before turning them out.