Warm the oven to 350°F (175°C). Lightly grease a 9×13-inch pan so the cake doesn’t stick. Mix the cake batter by blending the yellow cake mix with melted butter and three beaten eggs until smooth.
For the cream cheese layer, beat softened cream cheese with two cups of powdered sugar and a teaspoon of vanilla extract until creamy.
Spread half of the cake batter in the prepared pan. Carefully layer the cream cheese mixture over it, and then cover with the remaining batter.
Beat two more eggs in a small bowl and gently brush them over the top of the batter. This helps the cake develop a light golden sheen.
Bake for 40 to 45 minutes. Check doneness by inserting a toothpick into the center; it should come out clean. Let the cake rest in the pan on a wire rack for 15 to 20 minutes.
While the cake cools, prepare the frosting. Beat one cup of softened butter, adding three to four cups of powdered sugar gradually. Stir in two teaspoons of vanilla extract, one tablespoon of heavy cream, and a small pinch of salt. Keep mixing until smooth and fluffy. Adjust sugar or cream for the texture you like.
After the cake has cooled completely, spread the frosting evenly