In a small bowl, combine eggs and milk.
In a separate bowl, combine remaining 1/2 cup flour, salt and pepper.
In a large skillet or saucepan, heat frying oil to 375.
Dip each vegetable in the egg and milk mixture. and dredge in the flour and seasoning mixture. Finally, dip vegetables again into the beer and flour mixture. Place the vegetables in the oil and fry until golden brown.