Preheat oven to 350°F. Grease and flour a bundt pan or 9x5" loaf pan.
In the bowl of your electric mixer, combine cake mix and pudding mix.
Add eggs, melted and cooled butter, buttermilk, and vanilla. Beat on low for 30 seconds. Stop the mixer and scrape the sides and bottom of the bowl. Turn the speed to medium speed and beat for 2 minutes. The batter should be thick and creamy now. Stop the mixer and scrape the sides and bottom of the bowl. Mix on low just until everything is incorporated.
Stop the mixer and pour into your prepared pan. Smooth the top.
Bake at 350℉. Check with a wooden pick or cake thermometer beginning at 45 minutes - see notes below for more baking times. When the cake is done, remove and cool completely on a wire rack.