California Pizza Kitchen Butter Cake

1/2 Stick Unsalted Butter, Softened
1/3 C + 1/4 C Sugar
1 3/4 C Cake Flour
1 1/2 t Baking Powder
1/2 t salt
1 1/2 Sticks Unsalted Butter, Softened
1 C Sugar
1 Whole Egg and 1 Large Egg Yolk + 1 Egg
1 1/2 t + 1/4 t Vanilla Extract
3/4 C Whole Milk
1 8 Ounce Package Cream Cheese

Heat oven to 375.
Line a 9 Inch Springform Pan with parchment paper, clipping side onto the base after the paper. Trim excess. (Or cut a circle to fit a 9 inch round cake pan)
Rub the first 1/2 stick of softened butter on the bottom and sides of the pan, leaving a thicker layer on the bottom, as evenly as you can. Pour 1/3 cup sugar into the buttered pan, swirl it around to lightly coat the sides and leave a heavier, even coating on the bottom of the pan. Set aside.
Whisk together the flour, baking powder and salt.
With and electric mixer or in the bowl of a standing mix, beat the remaining 1 and 1/2 C butter and 1 cup of sugar until pale and fluffy (5 minutes).
Add egg and yolk and vanilla, beat until combined.
At a low speed, add flour mix and milk alternately until just combined.
Spread batter evenly in prepared pan.
Combine the cream cheese with the remaining 1/4 cup sugar, egg and 1/4 teaspoon vanilla. Mix well with a blender.
Gently spread over the top of the cake batter.
Bake 45-50 minutes until golden brown and a toothpick or fork comes out clean.
Cool cake in pan 10 minutes. Remove parchment paper and let cool.