- Make the pastry cream: In a saucepan over medium heat, bring milk, cream, vanilla, and salt to a boil. Cover pan, turn off heat, and set aside for 10 minutes. In a bowl, whisk egg yolks, sugar, and cornstarch until mixture is thick and pale. Continue to whisk while very slowly drizzling ¼ cup of the hot milk mixture into yolks. Once yolks are tempered, add remaining milk mixture in a steady stream and continue to whisk until combined. Remove and discard vanilla pod and transfer mixture to saucepan.
- Return pan to medium heat and bring to a boil while whisking vigorously. Keep mixture at a boil and whisk for 1 to 2 minutes more, then remove pan from heat and scrape pastry cream into a clean bowl. Allow cream to cool for about 3 minutes.
- Stir butter into hot pastry cream until it’s melted and incorporated. Press plastic wrap against surface of cream to create an airtight seal and refrigerate until completely chilled.
- Make the Tart Crust: In a food processor, pulse flour, sugar, and salt together. Scatter butter pieces over dry ingredients and pulse until butter is about the size of peas. In a small bowl, stir egg to break the yolk, then add to the food processor a little at a time, pulsing after each addition. Process until dough forms clumps. Turn dough out onto a work surface and very lightly knead to incorporate dry ingredients.
- Press dough evenly across the bottom and up the sides of a tart pan. Press firmly enough that the pieces cling to one another, but not so hard that the dough loses its crumbly texture. Freeze for at least 30 minutes.
- Preheat oven to 375 degrees. Butter a piece of aluminum foil and fit it tightly against crust. Place tart pan on a baking sheet and bake crust for 20 to 25 minutes, then carefully remove foil and discard. If crust has puffed, press it down gently with the back of a spoon. Bake crust about 10 minutes longer (or until it’s golden brown). Transfer pan to a rack and cool.
- Assemble the tart: Fill tart crust with pastry cream. Arrange berries decoratively on top of cream. In a small saucepan, melt apricot jam with 1 teaspoon water, then brush mixture over berries. Sprinkle with toasted pistachios and serve.