In a large shallow bowl, beat together the eggs and milk. Using a fork, dip the challah in the mixture, flipping it so that each side soaks up the egginess. Heat a skillet over medium-high heat and melt a good layer of butter in the pan. Working in batches, cook the challah on both sides until browned, adding more butter to the pan as needed. Season the French toast with salt and pepper on both sides.