In a food processor or large bowl, combine flour, 2 tablespoons sugar, and salt. Cut in the cold butter until the mixture resembles coarse crumbs.

Gradually add ice water, one tablespoon at a time, mixing until the dough just starts to hold together. Form into a disk, wrap in plastic, and chill for 30 minutes.

Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a large bowl, toss the sliced strawberries and rhubarb with 1/2 cup sugar, cornstarch, balsamic vinegar, and vanilla extract until evenly coated.

On a lightly floured surface, roll the chilled dough out into a 12-inch circle. It does not need to be perfect; rustic edges are part of the charm.

Transfer the dough to the prepared baking sheet. Pile the fruit mixture into the center, leaving a 2-inch border of dough all around.

Gently fold the edges of the dough over the fruit, pleating as you go to make it fit. The center of the fruit should remain exposed.

Brush the crust edges with the beaten egg and sprinkle with coarse sugar for crunch.

Bake for 40-45 minutes, or until the crust is golden brown and the fruit filling is bubbling.

Allow the galette to cool on the baking sheet for at least 15 minutes before slicing and serving.