Prepare the Tart Shell: In a food processor, pulse the flour, powdered sugar, and salt. Add cold butter cubes and pulse until the mixture resembles coarse meal. Add the egg yolk and pulse until the dough just comes together. Do not overmix. Form into a disk, wrap in plastic, and chill for at least 1 hour.

Blind Bake the Shell: Roll the chilled dough out to about 1/8 inch thickness and carefully line a 9-inch tart pan with a removable bottom. Trim the edges. Prick the bottom all over with a fork, then line with parchment paper and fill with pie weights or dried beans. Bake at 375°F (190°C) for 15 minutes. Remove the weights and parchment, and bake for another 10-12 minutes until light golden brown. Let cool completely.

Make the Pastry Cream: In a medium saucepan, heat the milk until simmering. In a separate bowl, whisk together the egg yolks, 1/4 cup of the sugar, and cornstarch until smooth and pale yellow. Slowly temper the hot milk into the egg mixture while whisking constantly.

Cook the Pastry Cream: Return the entire mixture to the saucepan. Whisk continuously over medium heat until the mixture thickens significantly and comes to a boil (it should bubble vigorously for 30 seconds to cook out the cornstarch taste). Remove from heat, stir in the remaining sugar, butter, vanilla extract, and vanilla bean paste. Press plastic wrap directly onto the surface of the cream and chill completely (at least 2 hours).

Assemble the Tart: Once the pastry cream is cold and firm, whisk it vigorously until smooth and creamy again. Spread the pastry cream evenly into the cooled tart shell.

Finish and Glaze: Arrange the mixed fresh berries decoratively over the pastry cream surface. In a small saucepan, gently heat the apricot jam with 1 tablespoon of water (or use clear glaze) until melted and liquid. Brush the warm glaze lightly over the berries to set them and give them shine. Chill the tart for 30 minutes before slicing and serving.