In a medium saucepan, warm the milk over medium-low heat until it begins to steam, then reduce the heat to low and keep it warm.
In a large mixing bowl, combine the egg yolks, sugar, salt, vanilla bean paste, and cornstarch. Whisk until the mixture becomes pale yellow and smooth.
Gradually incorporate a quarter of the warm milk into the egg mixture, stirring constantly, then add the rest and mix well.
Transfer this mixture back to the saucepan, cooking over medium-low heat while whisking continuously for 8-12 minutes, until thickened.
Remove from heat and mix in the butter until well combined. Place plastic wrap directly on top of the pastry cream and refrigerate until chilled.
Preheat your oven to 350°F and line two baking sheets with parchment paper.
In a large bowl, blend the flour, baking powder, and salt. Set aside.
Cream together the softened butter and 1 1/4 cups sugar with an electric mixer until fluffy, about 2 minutes.
Add the egg and vanilla bean paste, mixing on medium speed until the color lightens and the mixture becomes fluffy, around 1-2 minutes.
Gradually mix in the dry ingredients on low speed until the dough forms.
Using a cookie scoop, portion out the dough and roll into balls, then coat each in the remaining sugar.
Place the balls on your prepared sheets and lightly flatten each. Bake for 9-10 minutes, then cool on the baking sheet for 5 minutes before transferring to a wire rack.
After the cookies are cool, pipe the chilled pastry cream on top of each. Sprinkle with about a teaspoon of sugar per cookie and carefully use a kitchen torch to brûlée the sugar until golden and fragrant.
Allow to cool for another 10 minutes before serving. Best enjoyed immediately!