Using a medium pot, heat the milk, ½ C sugar and salt until warm to the touch
In a small bowl, whisk together the yolks, cornstarch and ¼ C sugar until combined
Slowly pour the warm milk into the egg mixture and whisk constantly
Pour the liquid into the pot and whisk some more for about 2-3 minutes over medium heat until thick
Pour into a mesh sleeve into another bowl
Cover with plastic wrap and place in the fridge overnight
Preheat oven to 350 and line a baking sheet with parchment paper
Using a standing mixer, beat the butter and sugar mixture together until combined and creamy
Beat in the eggs until combined
Using a medium bowl, whisk together flour, baking powder, and salt
Gradually mix in the dry ingredients while alternating with the milk and vanilla until combined
Using a medium ice cream scooper, scoop out some dough and place onto the cookie sheet
Bake in the oven for 13-15 minutes or until lightly browned
Allow to cool completely
Match the tops and bottoms of the cookies
Using a disposable piping bag, scoop the pudding into the bag
Cut the tip off
Pipe one hefty dollop of pudding into the middle of the bottom cookie
Place the top cookie on top and lightly push down