Before anything else, at 350 degrees Fahrenheit, preheat the oven. Then grease and line the cake pan.
Afterward, combine and whisk in a bowl the flour, baking powder, baking soda, salt, and a small package of instant French vanilla pudding mix.
In another bowl, whisk together the milk, oil, and vanilla extract.
Next, cream the butter and beat on medium speed until smooth in the bowl of your stand mixer fitted with a whisk attachment. At a low rate, slowly add the sugar and beat to medium-high speed for 2 minutes until fluffy.
Afterward, gradually add the eggs to the mixer one at a time until well incorporated at a low rate.
Using a rubber spatula, scrape down the bowl’s side from time to time and make sure the cream is well combined.
Afterward, alternately add in the flour mixture and the liquid mixture in a sequence at medium speed. After that, make sure to scrape down the bowl’s sides and whisk until the batter is well combined.
Then, be sure to turn the mixer off; using a rubber spatula, fold and scrape the batter until it is thoroughly mixed. After that, pour the batter and divide it into the prepared cake pans.
Bake at 350 degrees for 55 minutes.
Remove from the oven and invert to wire to rack to cool before entirely adding the frosting.