Heat the milk in a saucepan over medium-low heat until steaming. Reduce heat and keep warm.
In a large bowl, whisk egg yolks, sugar, salt, vanilla, and cornstarch until smooth and pale.
Slowly whisk in a portion of the warm milk, then add the rest. Return the mixture to the saucepan.
Cook over medium-low heat, whisking constantly, until thick with soft peaks.
Remove from heat, stir in butter, cover with plastic wrap directly on the surface, and chill completely.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Whisk flour, baking powder, and salt in a bowl.
Cream butter and sugar until light and fluffy. Add egg and vanilla and mix until pale.
Gradually mix in dry ingredients until just combined.
Scoop dough into balls, roll in sugar, place on baking sheets, and gently flatten.
Bake for 9–10 minutes. Cool completely.
Pipe chilled pastry cream onto each cookie. Sprinkle sugar on top and torch until caramelized. This step completes the signature Creme Brûlée Cookies finish.
Let set for 10 minutes before serving.