Pre-heat your oven to 375°F.
Place flour, sugar, salt, and butter into a bowl and cut the butter in until the size of large peas using a pastry cutter.
Slowly drizzle in ice water, gently incorporating each addition with a fork. After you add the fourth tablespoon, squeeze the dough together into a few handfuls. If it sticks, continue to form the dough into a disc. (If still too dry, add another tablespoon of water and then proceed to making the disc.) The dough should adhere and not be crumbly, but it also shouldn't be too wet.
Cover and chill the dough while making the filling.
Mix together rhubarb, strawberries, sugar, tapioca starch, cardamom, and vanilla extract. Mixture will appear very dry at first. Allow to macerate for 10 minutes.
Flour your surface and roll the dough into a large circle about 12 inches in diameter. Transfer to a parchment-lined baking sheet before adding fruit.
Mound strawberry-rhubarb mixture into the center of the dough, leaving behind excess liquid that has released from the fruit.
Fold the edges of the pie crust towards the center, leaving a small circle of exposed fruit.
Lightly whisk the egg together with a splash of water. Brush the egg wash over the crust and sprinkle with coarse sugar.
Bake on a parchment-lined baking sheet for 45 minutes until crust is firm and golden. Allow to cool for 15 minutes before serving.