Heat whole milk in a saucepan over medium heat until steaming but not boiling. In a separate bowl, whisk together egg yolks, granulated sugar, salt, vanilla bean paste, and cornstarch until pale and combined. Gradually whisk in hot milk, return mixture to saucepan, and cook over medium heat while stirring continuously until it thickens and bubbles gently, about 5 minutes. Remove from heat, stir in unsalted butter, and cool before refrigerating.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Combine flour, baking powder, and salt in a mixing bowl. In another bowl, cream together softened unsalted butter and granulated sugar for about 3 minutes until light and fluffy. Beat in egg and vanilla extract. Gradually add dry mixture to wet ingredients, stirring until just incorporated.

Using a cookie scoop, portion dough into balls and roll each in sugar to coat. Place on prepared sheets, flatten slightly, and bake for 9-10 minutes or until edges are light golden. Allow to cool on sheets before transferring to a wire rack.

Once cooled, transfer chilled pastry cream to a piping bag and pipe a dollop onto each cookie. Sprinkle sugar over pastry cream, aiming for about 1 teaspoon per cookie.

Using a kitchen torch, caramelize the sugar on the pastry cream until melted and golden brown, moving the torch to ensure even caramelization. This process should take about 1-2 minutes per cookie.

Allow cookies to cool for a few minutes before serving, letting the caramel crust harden slightly. Enjoy immediately.