Make the Vanilla Pastry Cream
In a medium saucepan, heat the milk over medium-low heat until steaming. Reduce heat to low and keep warm.
In a large bowl, whisk together the egg yolks, sugar, salt, vanilla bean paste, and cornstarch until smooth and pale yellow.
Slowly whisk in about ¼ of the warm milk to temper the eggs.
Gradually whisk in the remaining milk until fully combined.
Return the mixture to the saucepan and cook over medium-low heat, whisking constantly for 8–12 minutes, until thick and soft peaks form.
Remove from heat and transfer to a bowl.
Stir in the cubed butter until smooth.
Press plastic wrap directly onto the surface and refrigerate until completely chilled.
Make the Sugar Cookies
Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the softened butter and sugar until light and fluffy, about 2 minutes.
Add the egg and vanilla bean paste. Beat until pale and fluffy, about 1–2 minutes.
Gradually add the dry ingredients and mix on low speed until a soft dough forms.
Scoop the dough into large portions and roll into balls.
Roll each dough ball in the reserved sugar.
Place on the prepared baking sheets and gently flatten each ball.
Bake 6 cookies per sheet for 9–10 minutes.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Assemble the Cookies
Transfer the chilled pastry cream to a piping bag fitted with a small round tip.
Pipe a generous swirl of pastry cream onto each cooled cookie.
Sprinkle about 1 teaspoon of sugar over the pastry cream.
Using a kitchen torch, carefully caramelize the sugar until golden brown and crisp.
Allow the cookies to rest for 10 minutes before serving.