In a food processor or a bowl, combine 2 cups flour, 1/4 cup sugar, and salt. Cut all but 2 teaspoons butter into small pieces and add to flour mixture. Whirl or rub in with your fingers until fine crumbs form. Add 1/4 cup water; whirl or stir with a fork just until dough holds together. Pat into a smooth 5-inch round. Wrap airtight and freeze until slightly firm, about 15 minutes.
Meanwhile, in a bowl, gently mix strawberries, rhubarb, 1/2 cup sugar, 3 tablespoons flour, and cardamom.
On a lightly floured board, roll dough into a 14-inch round. Slide onto a 14- by 17-inch baking sheet; if dough tears, press back together.
Stir berry mixture; spoon evenly onto pastry, leaving a 3-inch border. Fold dough border over edges of fruit, tucking to incorporate excess pastry.
Melt remaining 2 teaspoons butter in a microwave-safe bowl in a microwave oven at full power (100%), about 15 seconds. Brush pastry rim with butter and sprinkle with 1 teaspoon sugar.
Bake in a 375° regular or 350° convection oven until pastry is browned and fruit bubbling, 40 to 45 minutes.
Let cool at least 30 minutes. Slide a long metal spatula under pastry to release. Slide pie onto a platter. Serve warm or cool. Cut into wedges.