Unfold piecrust, and roll into a 12-inch circle on a lightly greased baking sheet. Fold outer 2 inches of dough over, and crimp. Prick bottom of crust with a fork.
Bake at 425° for 8 to 10 minutes or until lightly browned.
Remove root, tough outer leaves, and tops from leeks, leaving 2 inches of dark leaves. Thinly slice leeks; rinse well, and drain.
Sauté leeks in hot oil in a skillet over medium heat 8 to 10 minutes or until tender. (Do not brown.) Stir in cream, salt, and pepper; cook, stirring constantly, 4 to 5 minutes or until slightly thickened. Stir in tarragon.
Sprinkle 2 ounces (1/2 cup) goat cheese on bottom of crust; top with leek mixture. Sprinkle with remaining cheese.
Bake at 375° for 18 to 20 minutes or until golden and bubbly.