Wash leek in a bowl of cold water, agitating water, then lift out leek and pat dry.
Cook asparagus in a wide 4- to 5-quart pot of boiling salted water, uncovered, until just tender, about 5 minutes. Transfer asparagus with tongs to a bowl of ice and cold water to stop cooking, then drain and pat dry. Cut off and reserve tips (leave more stalk if asparagus is thin), then thinly slice stalks crosswise.
Heat butter in a 10- to 12-inch heavy skillet over moderately low heat until foam subsides, then cook leek with 1/4 teaspoon salt, stirring, until softened, 6 to 8 minutes. Stir in sliced asparagus and 1/4 teaspoon pepper and remove from heat.
Put oven rack in middle position and preheat oven to 375°F.
Whisk together cream, 2 eggs, tarragon, and remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Lightly beat remaining egg with water in a small bowl and brush pie shell all over with some egg wash. Spoon asparagus mixture into shell, spreading evenly, then pour cream mixture over asparagus.
Bake until filling is just beginning to set but still loose on top, 20 to 25 minutes. Scatter asparagus tips over top, pressing lightly if necessary to help them settle into filling, then continue to bake until custard is golden and just set but still slightly wobbly in center, about 30 minutes more (custard will continue to set as it cools).
Cool on baking sheet on a rack until warm, about 30 minutes. Loosen edge with a small sharp knife. Serve warm or at room temperature, cut into wedges.