Line a 9-inch quiche dish with pastry; trim excess pastry around edges. Prick bottom and sides of pastry with a fork. Bake at 400F for 3 minutes; remove from oven, and gently prick with a fork. Bake 5 more minutes. Set aside.
Cook broccoli according to package directions, omiting salt; drain well. Layer half each of broccoli, ham, and cheese in pastry shell; repeat layers. Sprinkle onion evenly over top.
Combine eggs and remaining 3 ingredients; stir with a wire whisk until blended. Pour over layers in pastry shell. Bake at 450F for 10 minutes. Reduce oven temp to 325F and bake 30 minutes or until set and golden. let stand 10 minutes.