Spray 13x9-inch baking dish with cooking spray; cover bottom with 6 bread slices. Top with layers of half each of the ham, broccoli, onions and Singles pieces. Cover with remaining bread slices. Repeat layers of ham, broccoli and onions.
Beat eggs and pepper in medium bowl with whisk until blended. Gradually beat in milk; pour over ingredients in baking dish. Cover. Refrigerate 3 hours.
Heat oven to 350°F. Bake, uncovered, 45 min. Top with remaining Singles pieces; bake 15 min. or until knife inserted in center comes out clean. Let stand 10 min. before cutting to serve.