1. In a large bowl, whisk together 2 cups flour, 2 teaspoons sugar, and 1 teaspoon salt. With a snapping motion, use your fingers to incorporate butter into flour mixture. Make a well in center of flour and add water. Mix until dough just begins to hold together. Turn out onto a clean, lightly floured work surface. Press dough into a flat disk, wrap in plastic, and refrigerate for 1 hour.
2. Preheat oven to 375 degrees before removing dough from fridge. On a clean, lightly floured work surface, roll dough to 1⁄8-inch thickness. Gently roll well-floured round onto rolling pin and transfer to a 10-inch skillet. Unroll dough over a skillet. Instead of stretching dough into pan, lift and place it into the bottom and against the sides. Use a knife to trim edges to 2 inches larger than skillet.
3. Toss cut plums with remaining flour, sugar, and salt. Pour plums into skillet and arrange into an even layer. Fold dough over itself to form pleats. Optionally, brush with heavy cream or beaten egg whites and dust with coarse sugar. Bake until crust is golden and filling is bubbling, about 1 hour. Let cool on a rack before serving.