To make the dough: Blend together flour, butter, sugar, and salt in a bowl with your fingertips or a pastry blender until mixture resembles coarse meal with some small (roughly pea-size) butter lumps. Drizzle evenly with 2 tablespoons ice water and gently stir with a fork until incorporated.
Squeeze a small handful: If it doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring until just incorporated, then test again. (Do not overwork mixture, or pastry will be tough.)
Turn out mixture onto a lightly floured surface and divide into 4 portions. With heel of your hand, smear each portion once or twice in a forward motion. Gather dough together with scraper and press into a ball, then flatten into a 5-inch disk. Chill, wrapped in plastic wrap, until firm, at least 1 hour.
Roll out dough with a floured rolling pin into a 14-inch round on a lightly floured surface, then fit into tart pan. Trim excess dough, leaving a 1/2-inch overhang, then fold overhang inward and press against side of pan to reinforce edge. Chill 30 minutes.
To make filling while the shell chills: Stir together sugar and cornstarch in a large bowl. Add plums and lemon juice and toss to coat. Let stand, stirring occasionally, 30 minutes, or until juicy.
To assemble and bake tart: Preheat oven to 425 degrees F.
Arrange plum halves, skin sides down, in tart shell, overlapping in a rosette pattern. Halve any remaining plums lengthwise and randomly tuck in between plum halves in tart. Pour all juices from bowl over plums.
Bake tart in middle of oven 15 minutes, then reduce temperature to 375 degrees F. Cover tart loosely with foil and bake until plums are tender and juices are bubbling and slightly thickened, 40 to 50 minutes more. Brush warm juices in tart over plums. (Juices will continue to thicken as tarts cool.) Cool tart completely in pan on a rack.