Place parchment paper or a silicone baking mat on a work surface, dust with flour and turn the dough out onto it. Dust the dough with flour and roll into a rough 9-inch circle, dusting with flour as necessary to prevent sticking. Transfer paper or mat and the crust to a baking sheet.
Toss strawberries with sugar, 1 teaspoon flour, cornstarch, pepper and salt in a medium bowl. Mound the strawberry mixture in the center of the crust, leaving about a 2-inch border around the outside. Pick up the edges of the crust using a spatula and fold over the berries. (The crust will not meet in the center.)
Bake the tart until the crust is lightly browned and the filling is bubbling, 40 to 42 minutes. Let cool on the baking sheet for 15 minutes before serving.
Look for whole-wheat pastry flour in the natural-foods section of large supermarkets and natural-foods stores. Sources include King Arthur Flour, (800) 827-6836, www.bakerscatalogue.com, and Bob's Red Mill, (800) 349-2173, www.bobsredmill.com.