Line an 8x8 inch square baking pan with parchment paper. Preheat the oven to 350℉.
Add the flour, baking powder, and kosher salt into a bowl. Whisk the ingredients together until combined. Set aside.
In a separate bowl, cream together the butter and sugar until fluffy. Mix in the eggs and vanilla extract until well combined. Pour in the bowl of dry ingredients and fold everything together until you get a dough.
Add half of the dough into the lined baking pan. Lightly flour your hands and press the dough out into an even layer, covering the bottom of the pan. Spread the cream cheese mixture on top. Add the remaining half of the cookie dough on top and use floured hands to gently spread the dough into an even layer, completely covering the cream cheese. Try to be gentle so you do not disturb the cream cheese layer.
Bake it in the oven for about 38 minutes until the edges are lightly golden and a toothpick inserted into the center comes out clean. Remove the sugar cookie bars from the oven and allow it to cool completely in the pan.