In a medium saucepan, combine heavy cream, granulated sugar, and pure vanilla bean paste. Heat over medium until the mixture simmers gently, stirring frequently. Whisk egg yolks until pale, then slowly incorporate the hot cream mixture to temper the eggs. Return to the saucepan and cook until thickened, about 5-7 minutes, then transfer to a bowl to cool completely.

In a large mixing bowl, cream together unsalted butter, granulated sugar, and brown sugar using an electric mixer until light and fluffy, roughly 2-3 minutes. Beat in eggs one at a time along with vanilla until fully combined. Gradually mix in sifted flour, baking powder, and salt until just incorporated.

Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 30 minutes. Preheat your oven to 350°F (175°C).

Remove the dough and scoop tablespoon-sized portions, rolling them into balls. Arrange on baking sheets lined with parchment paper. Bake for 10-12 minutes, until edges are lightly golden.

Let cookies cool for about 5 minutes, then create a small well in the center of each cookie and fill with cooled pastry cream.

Evenly sprinkle a layer of granulated sugar over the pastry cream filling of each cookie. Using a kitchen torch, caramelize the sugar until crispy and golden brown.