In 4-quart saucepan, heat broth, milk and pepper to boiling. Slowly stir in grits. Reduce heat to low; cover and cook 6 to 8 minutes, stirring occasionally, until thickened and no lumps remain. Remove from heat. Stir in 1 1/2 cups of the cheese until melted. Stir in ham, 1/2 cup green onions and the eggs; transfer to baking dish.