In a medium bowl, mix together 1-1/2 cup flour and beer with a wooden spoon; let stand for at least 3 hours at room temperature.
Mix eggs and milk in a small bowl. In a separate bowl, mix together 1/2 cup flour and salt and pepper.
Heat oil to 375 degrees F (190 degrees C). Dip each vegetable in the egg and milk mixture. Next dip the vegetable into the flour and seasoning mixture, finally dip the vegetable in the beer and flour mixture.
Place the vegetables into the oil and fry until golden brown.