In a medium saucepan, heat 2 1/4 cups of whole milk over medium-low heat until steaming. Meanwhile, whisk 6 egg yolks, 1 cup and 2 tablespoons of granulated sugar, 1/8 teaspoon of salt, 3 1/2 tablespoons of cornstarch, and 1 1/2 tablespoons of vanilla bean paste in a separate bowl until smooth. Gradually mix in the warm milk, then return the mixture to the saucepan and cook on medium-low for 8-12 minutes, whisking continuously until thickened. Remove from heat, stir in 3 tablespoons of unsalted butter, and chill covered in the refrigerator.

Preheat your oven to 350°F (175°C) while you mix your cookie dough. In a medium bowl, whisk together 2 1/2 cups of all-purpose flour, 1/2 teaspoon of baking powder, and 1/2 teaspoon of salt. In a large mixing bowl, beat 1 cup of unsalted butter and 1 1/4 cups of granulated sugar together until light and fluffy. Add in 1 egg and 1 tablespoon of vanilla extract, mixing until combined, before gradually incorporating the dry ingredients until just combined.

Once your dough is ready, scoop out portions and roll them into balls, about 1 tablespoon each. Roll each ball in 1/2 cup of granulated sugar to coat them evenly. Arrange the coated cookie balls on parchment-lined baking sheets, giving them enough space to spread, and gently flatten each ball with your palm to create a slightly thicker cookie shape.

Place the baking sheets in the preheated oven and bake the cookies for 9-10 minutes, or until the edges are a light golden brown while the centers remain soft. Once baked, remove them from the oven and let them cool for about 5 minutes on the baking sheets before transferring them to a wire rack to cool completely.

When the cookies are completely cooled, pipe the chilled pastry cream generously on top of each cookie. Next, sprinkle a thin layer of granulated sugar over the pastry cream. Using a kitchen torch, carefully caramelize the sugar until it reaches a golden brown color and becomes crisp. Let the cookies cool slightly before serving.