In a medium saucepan, whisk together egg yolks, granulated sugar, and a pinch of salt until pale and creamy. Gradually add cornstarch while whisking continuously. Slowly stir in whole milk and place over medium heat. Cook for 8-10 minutes until thickened. Remove from heat and mix in butter, vanilla bean paste, and lemon zest. Cool for 30 minutes, then refrigerate for at least 2 hours.

In a large mixing bowl, cream unsalted butter and granulated sugar until fluffy, about 3-4 minutes. Beat in egg yolks and remaining vanilla extract. In a separate bowl, combine all-purpose flour, baking powder, baking soda, and salt. Fold flour mixture into wet ingredients until just combined.

Fold half of the chilled custard into the cookie dough gently until evenly incorporated, creating a creamy center with visible swirls of custard.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Drop heaping spoonfuls of dough onto sheets, spacing 2 inches apart. Bake for 10-14 minutes until edges are golden and centers remain soft. Cool for 5 minutes before transferring to finish cooling.

Sprinkle granulated sugar over cooled cookies. Using a kitchen torch, caramelize sugar until deep amber and crackly. Alternatively, place under broiler, watching closely. Let caramelized sugar set for a few minutes before serving.