Combine flour, sugar, salt and vanilla bean seeds in the bowl of a food processor. Cut chilled butter into small cubes; add to food processor and pulse until combined, about 10 times. Cut frozen butter into small cubes; add to food processor and pulse just until a coarse meal with a few larger chunks of butter forms.

Add ice water to food processor and pulse just until a dough forms, about 10 times. Turn out dough onto a countertop and form dough into a disk. Place disk between two large pieces of plastic wrap; roll out to a 1/2-inch thick round. Seal in plastic wrap and chill at least 45 minutes or up to 2 days (can also be wrapped in plastic, then foil, and frozen up to a month).

When dough is fully chilled, unwrap and roll out on a floured surface to a 1/4-inch thick round. Cut dough into a 10-inch circle; discard scraps. Transfer dough disk to a lightly floured sheet of parchment paper on a baking sheet. Chill for 30 minutes.

Heat oven to 350 degrees F. Toss hulled and sliced strawberries with sugar and cornstarch. Immediately place strawberries on chilled dough, slightly overlapping in concentric circles, if desired, leaving a 1-inch border along the edges. Carefully fold up dough around the sides. Chill for 15 minutes.

Brush dough with egg wash, then sprinkle with 2 teaspoons sugar. Sprinkle chilled butter pieces over berries. Bake until golden brown and filling is bubbly, about 45 minutes. Cool to room temperature on a cooling rack. Serve with fresh whipped cream and top with snipped fresh basil just before serving, if desired.