In a non-reactive bowl, whisk together the eggs and milk. In a separate bowl mix the flour and salt. In a small sauce pot or saute pan over low heat melt the butter and cook it until it is light brown.
Add the egg and milk mix to the flour and salt and mix well so that there are no large clumps. Add the browned butter and mix to incorporate, being careful not to overwork batter. The batter should just coat the back of a spoon. If seems too thick, thin it out with a little more milk or water. Let the batter rest for 1 hour prior to cooking crepes.