In a large bowl, whisk the eggs until combined. Whisk in the milk, beer and melted butter. Scatter the flour and salt over the mixture and whisk until smooth, about 2 minutes (the batter should be the consistency of heavy cream). Cover the bowl and let the batter rest for 1 hour at room temperature or refrigerate overnight.
In a small nonstick skillet, melt the remaining 1/2 teaspoon butter. Using a ladle, stir the batter and pour a scant 1/3 cup into the pan, rotating and tilting the pan to form a thin crepe. Cook the crepe until golden on the bottom, 1 to 2 minutes. Using a spatula, flip the crepe and cook for 30 to 60 seconds more. Repeat with the remaining batter, cooking each crepe after the first few for about 30 seconds on each side. Cover the crepes with a towel to keep warm.