01 - Using an electric mixer, beat the softened butter and powdered sugar together in a large bowl until the mixture becomes pale, smooth, and fluffy, approximately 3 minutes. Incorporate the vanilla extract and mix until fully combined.
02 - Sift the all-purpose flour and salt directly into the butter mixture. Mix on low speed or fold by hand until just combined and a cohesive dough forms, being careful not to overwork the dough.
03 - Divide the dough into two equal portions and shape each into a log approximately 2 inches in diameter. Wrap each log tightly in plastic wrap and refrigerate for a minimum of 30 minutes or until firm enough to slice cleanly.
04 - Preheat the oven to 350°F. Line two large baking sheets with parchment paper, ensuring complete coverage to prevent sticking during baking.
05 - Remove one dough log from the refrigerator at a time. Using a sharp knife, slice the dough into rounds approximately 1/2 inch thick. Arrange the slices on the prepared baking sheets, leaving 1 inch of space between cookies to allow for slight spreading.
06 - Place the baking sheets in the preheated oven and bake for 12 to 14 minutes, or until the edges begin to turn a light golden color. Remove from the oven and let the cookies cool completely on the baking sheets before transferring.
07 - While cookies cool, combine egg yolks, 1/4 cup granulated sugar, heavy cream, and vanilla bean paste in a small saucepan. Whisk thoroughly until smooth. Place over medium-low heat and stir continuously with a whisk or silicone spatula for 4 to 5 minutes until the mixture slightly thickens and coats the back of a spoon. Remove immediately from heat and transfer to a clean bowl. Let cool completely at room temperature.
08 - Using a small spoon or offset spatula, place a small dollop of the cooled custard onto the center of each completely cooled shortbread cookie. Gently spread the custard to create an even layer, leaving a small border around the edges.
09 - Sprinkle a thin, even layer of granulated sugar over the custard topping on each cookie. Using a kitchen torch, caramelize the sugar by holding the flame approximately 2 inches from the surface and moving in a circular motion until the sugar melts and turns a deep golden amber color. Allow the caramelized sugar to harden for at least 5 minutes before serving.