To assemble tart, pour pastry cream into baked crust in a smooth, even layer. Top with berries.
Raspberry pastry cream. In a 1 1/2- to 2-quart pan, mix 1/2 cup sugar with 2 tablespoons cornstarch, 3 tablespoons flour, and a pinch salt. Whisk in 2 1/2 cups whole milk, then add 1 large egg and 2 large egg yolks. Whisk until smooth. Place over high heat and stir constantly with a wooden spoon until mixture boils and becomes quite thick, 4 to 6 minutes. Remove from heat and stir in 1 tablespoon raspberry-flavored liqueur, such as Chambord, and 1 1/2 tablespoons unsalted butter. Pour mixture through a strainer into a medium bowl; set bowl in ice water and stir often until pastry cream is cool, about 12 minutes. Keep chilled.
Butter crust. Preheat oven to 300°. In a food processor or a bowl, combine 1 1/3 cups all-purpose flour, 1/4 cup sugar, and 1/4 teaspoon salt. Add 8 tablespoons (1/2 cup) chilled unsalted butter, cut into small cubes; whirl (or rub with your fingers) until fine crumbs form. Add 1 large egg yolk; whirl (or mix with a fork) until dough holds together. Firmly press the dough into bottom and up sides of a 10-inch tart pan with removable rim. Bake until golden, 25 to 30 minutes; let cool.