In a food processor, whirl flour and butter until mixture looks like cornmeal. Add 1 egg and whirl until dough holds together. Press evenly over bottom and 1 1/4 in. up side of a 9-in. springform pan; chill.
Preheat oven to 375°. Soak mushrooms in a small bowl with 1 cup hot water until softened, 15 to 20 minutes, swishing them around every so often. Gently squeeze out liquid. Cut in half lengthwise if large. Save liquid for another use.
Blanch asparagus in a saucepan of boiling water until barely tender-crisp, about 45 seconds. Drain, transfer to a bowl of ice water, and cool. Drain and pat dry.
In a bowl, whisk remaining 2 eggs to blend. Whisk in half-and-half, salt, and pepper. Sprinkle gruyère and onion in prepared crust, then arrange asparagus and morels on top. Pour egg mixture over vegetables.
Bake quiche on bottom rack until filling no longer jiggles when gently shaken, 40 to 45 minutes. Let cool in pan on a rack at least 30 minutes. Loosen quiche from pan rim with a knife, remove rim, and slice. Serve warm or at room temperature.
Note: Nutritional analysis is per serving.