Combine the rhubarb, strawberries, sugar, lemon juice, cornstarch, water, and ground ginger in a saucepan over medium-low heat. Stir occasionally and cook for 10-12 minutes until the mixture thickens and the fruit breaks down slightly. The filling should bubble gently and coat the back of a spoon. Transfer to a bowl and let cool completely—this can be done while you make the pastry, or even the day before. I like to make the filling first so it's cooled and ready when I need it, which prevents the dough from getting warm during assembly.

Mix the flour and salt in a large bowl. Add the cold grated butter and use your fingertips to rub it into the flour until the mixture resembles coarse breadcrumbs with pea-sized pieces of butter still visible—this texture is crucial for flaky layers. Add the ice-cold water a tablespoon at a time, mixing gently with a fork until the dough just comes together. Do not overwork the dough. Form it into a round disc, wrap in plastic wrap, and refrigerate for 2 hours. The cold butter and minimal handling create steam pockets during baking that make the pastry flaky.

Remove the chilled dough from the refrigerator and roll it into a 6x12 inch rectangle on a lightly floured surface. Fold the dough into thirds like a letter (fold one short end over, then fold the other short end on top), then rotate it 90 degrees and roll again into a 6x12 inch rectangle. Repeat this fold-and-roll process 3 times total. Each fold creates more layers of butter and dough, which produces the characteristic flaky texture. After the final fold, wrap the dough and refrigerate for 30 minutes before the final rolling and cutting.

Roll the laminated dough into a 12-inch square on a lightly floured surface and cut it into 4-inch squares—you should get 9 squares. Place about 1 tablespoon of cooled filling from Step 1 on one corner of each square, then fold the square diagonally to form a triangle and press the edges together. Use a fork to crimp and seal the edges, which helps prevent the filling from leaking during baking. Arrange the turnovers on a parchment-lined baking sheet and refrigerate for 15 minutes while you preheat the oven. I like to make sure the edges are well-sealed because a burst turnover loses all its appeal.

Preheat the oven to 400°F. While the oven heats, whisk together the egg and 1 tablespoon of water to make an egg wash. Brush the egg wash over each turnover, then use a sharp knife to cut three small slits in the top of each one—these vents allow steam to escape and prevent the pastry from bursting. Bake for 20-22 minutes until the turnovers are golden brown and puffed. Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

While the turnovers cool, prepare the glaze by beating together the softened cream cheese, icing sugar, vanilla, milk, and pinch of salt until smooth and pourable. If the glaze is too thick, add milk one tablespoon at a time until you reach the right consistency. Once the turnovers are completely cooled, drizzle or pour the glaze over the top of each one. I prefer Philadelphia brand cream cheese because it creates a smoother, more luxurious glaze without any graininess.