In a small bowl, vigorously whisk together the egg yolks, sugar, cornstarch, ¼ cup of milk, and 1 tsp of Diamond Crystal or ½ tsp of Morton kosher salt until well combined.
In a medium saucepan, heat the remaining 2 cups of milk over medium heat until it starts to steam.
Carefully pour the egg yolk mixture into the saucepan, scraping the bowl with a spatula to ensure you get every bit. Cook while whisking constantly, making sure to reach the corners of the pan, until the mixture bubbles and thickens, which should take about 3 minutes.
Lower the heat to low and let it simmer for an additional minute while whisking constantly.
Remove the saucepan from the heat and add the butter and vanilla bean paste, whisking until the butter has melted and the pudding is smooth.
Transfer the pudding to a large bowl and cover it with plastic wrap, pressing it directly onto the surface to prevent a skin from forming. Chill in the refrigerator until cold, approximately 30 minutes.
In a medium bowl, use an electric mixer on medium-high speed to beat the chilled heavy cream and the remaining 1 tsp of Diamond Crystal or ½ tsp of Morton kosher salt until stiff peaks form, which should take about 5 minutes.
Beat the chilled pudding with the electric mixer until it becomes smooth and glossy, about 45 seconds. It may appear clumpy at first, but it will quickly become smooth.
Stir one quarter of the whipped cream into the pudding to loosen it, then gently fold in the remaining whipped cream.
Set aside 4 or 5 cookies for serving. In a medium bowl, stir the jam to loosen it, then gently fold in the fresh berries.
Spoon one third of the whipped pudding into a medium serving bowl or dish. Add a layer of cookies, breaking each into 2–3 pieces, followed by half of the berry mixture.
Repeat the layers once more, using half of the remaining whipped pudding, and then top with the rest of the whipped pudding.
Lightly crush the reserved cookies and sprinkle them on top. Cover with a silicone lid or plastic wrap and chill for at least 6 hours before serving.
For best results, you can assemble the pudding a day in advance and keep it chilled.
