Step 1

Vigorously whisk egg yolks, sugar, cornstarch, ¼ cup milk, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a small bowl to combine. Heat remaining 2 cups milk in a medium saucepan over medium until steaming. Pour in egg yolk mixture, scraping bowl with a spatula to get every last bit, and cook, whisking constantly and making sure to get into corners of pan, until bubbling and thickened, about 3 minutes.

Step 2

Reduce heat to low and continue to simmer, whisking constantly, 1 minute. Remove from heat; add butter and vanilla bean paste and whisk until butter is melted and pudding is smooth. Scrape pudding into a large bowl and cover with plastic wrap, pressing directly onto surface to prevent a skin from forming. Chill until cold, about 30 minutes.

Step 3

Using an electric mixer on medium-high speed, beat cream and remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in medium bowl until stiff peaks form, about 5 minutes.

Step 4

Using electric mixer, beat chilled pudding until smooth and glossy, about 45 seconds. (It may look clumpy and broken initially, but don’t worry. It will quickly smooth out.) Stir one quarter of whipped cream into pudding to loosen, then fold in remaining whipped cream.

Step 5

Set 4 or 5 cookies aside for serving. Stir jam in a medium bowl to loosen; gently fold in fresh berries.

Step 6

Spoon one third of whipped pudding into a medium serving bowl or dish. Top with a layer of cookies, breaking each into 2–3 pieces. Top with half of berries. Repeat layers once more, using half of remaining whipped pudding. Top with remaining whipped pudding. Lightly crush reserved cookies and sprinkle over. Cover with silicone lid or plastic wrap; chill at least 6 hours before serving.Do ahead: Pudding can be assembled 1 day ahead. Keep chilled.