In a large bowl, whisk together eggs, milk and beer. Gradually whisk in flour. Add the salt and oil, then whisk the batter vigorously for 3 to 5 minutes, so all is thoroughly incorporated. Let the batter sit for 1 hour.
Heat a 10 inch non-stick skillet over medium heat. Brush it with butter, and when it's hot but not smoking, pour a scant 1/3 cup of batter into the center of the skillet, and rotate it so the batter covers the bottom of the pan in a thin layer, pouring out any excess batter. Cook the crepe until it is just golden on one side, 1 to 2 minutes, turn it and cook until it is golden on the other side, about 30 seconds. Transfer to a plate, and keep warm by covering with aluminum foil. Continue until all of the batter is used.