Preheat the oven to 350F and line a baking sheet with parchment paper.
In a large mixing bowl, using an electric mixer, cream the butter until smooth. In portions, add both the white and brown sugar and mix well before adding more sugar each time. Mix with a hand mixer until well combined.
Add the egg and vanilla extract to the butter and sugar mixture and mix until smooth.
All at once, add the dry ingredients - flour, baking powder, and salt to your large bowl and mix until you get a thick sugar cookie dough.
Use a cookie scoop to create cookie dough balls and put them on the prepared baking sheet about 2-inches apart.
Use your hands to press the cookie dough ball down slightly.
Bake cookies for 13 minutes or until the edges turn a light brown.
Make the vanilla creme as the sugar cookies bake.
First, in a saucepan or pot, add the heavy cream and whole milk over medium heat until it starts to steam. Decrease the heat to low heat while you make the egg mixture in a small bowl.
Add the eggs, sugar, salt, and cornstarch to a small bowl and whisk together until it becomes a pale yellow.
Remove the milk mixture from heat and temper ¼ cup of the milk mixture into the egg mixture in the small bowl while you whisk.
Then carefully temper the rest of the milk into the egg mixture before pouring it all back into the saucepan.
Over medium heat, place the saucepan with the combined mixtures and stir continuously for about 8 minutes, or until it thickens.
Then remove the saucepan from the heat and add in the butter, stirring until it melts.
Pour the vanilla creme into a bowl, cover with plastic wrap and refrigerate for an hour.
Transfer cooled vanilla creme to a piping bag and cut the tip.
Pipe the cream onto the top of each of the cookies and then generously cover the creme on top of each cookie with granulated white sugar.
Using a kitchen torch or a small butane torch, carefully brulee the tops of each cookie until the cream on top of the cookie turns a beautiful golden brown.
Let them cool while the creme brulee hardens for a couple of minutes before enjoying.