Whisk the sugar, cornstarch and salt in a medium bowl. Slowly pour in half the heavy cream, while whisking continuously to dissolve the dry ingredients. Slowly pour in the remaining cream, whisking continuously.
Slowly pour the milk into the bowl, whisking continuously, making sure that the dry ingredients are completely dissolved. Pour the mixture into a small saucepan and clean and wipe the bowl.
Heat the mixture over medium heat, stirring constantly with a wooden spoon and making sure to scrape along the sides and bottom. When the mixture comes to a simmer, reduce the heat to low and continue stirring for 1 minute. Remove from the heat and stir in the vanilla, butter and vanilla bean seeds.
Pour the mixture back into your now-clean bowl, place plastic wrap directly onto the surface and refrigerate for a minimum of 4 hours.
Make the hamantaschen dough:
Beat the butter, cream cheese and sugar till fluffy. Add one egg, the vanilla and salt – beat again. Add the flour and beat just till incorporated. Separate the dough into two halves and place each between two sheets of parchment paper. Roll each dough to about 1/4″ thickness. Stack the doughs on a baking sheet or cutting board and refrigerate for at least one hour, or up to three days.
Make the hamantaschen:
Beat the remaining egg with one tablespoon of water.
Working with one dough at a time, place on a baking sheet and remove the top piece of parchment paper. Cut out circles with a drinking glass or cookie cutter (I used a 2 1/2″ cutter here). Remove the trimmings and keep re-rolling and cutting till all the dough is used up. Repeat with the other dough and a second baking sheet.
Place 1/2 teaspoon of the vanilla bean filling into the center of each circle. Fold the dough into a triangle shape and pinch the corners firmly together to almost completely close the cookie. Brush the tops of the cookies with a little of the beaten egg and sprinkle with the granulated sugar. Freeze for several hours, ideally overnight.
Pre-heat the oven to 375 degrees.
Bake the cookies, one sheet at a time, for about 10 minutes or till light golden brown. Let cool completely on the baking sheets.
Make the brulee topping:
Place the sugar in a small saucepan and heat, undisturbed, over medium-high heat. Once the sugar begins to liquify around the edges, start moving that liquid into the dry sugar, and begin stirring with a heatproof spatula or wooden spoon. Continue stirring until almost all of the sugar is dissolved. Turn off the heat and continue stirring until no more dry sugar remains. Immediately pour the caramel over the center of each cookie, letting it run over the sides. Let the caramel harden completely before serving.
Notes
You can substitute boxed vanilla pudding for the vanilla bean filling if you prefer.