Heat oven to 400 degrees F. Grease pie plate. Riince broccoli; drain thoroughly. Mix broccoli 2/3 of cheese, chicken, and onion in pie plate.
Blend milk, eggs, baking mix, salt and pepper until smooth. Pour into pie plate. Bake until knife inserted in center comes out clean, 30 to 40 minutes.
Top with remaining cheese.
Bake just until cheese is melted, 1 to 2 minutes longer.