Combine flour, salt, and xanthan gum in a bowl. Whisk eggs and milk together in a separate bowl. Make a well in the flour mixture and pour egg mixture in the center; mix until slightly combined. Add melted butter and mix until a soft batter is formed, 1 to 2 minutes. Cover and let stand for 45 minutes.

Melt butter in an 8-inch skillet over medium heat. Pour 2 tablespoons of batter into the skillet and immediately rotate the skillet to spread batter out in a thin layer. Cook until the top of the crepe is no longer wet and the bottom has turned light brown, 1 to 2 minutes. Run a spatula around the edge of the skillet to loosen crepe; flip crepe and cook until the other side has turned light brown, about 1 minute more.