Place eggs, cream cheese, Parmesan cheese, and erythritol in a blender; blend on low until ingredients are completely combined. Sprinkle in coconut flour and xanthan gum while blender runs. Continue blending until thick, scraping the sides of the blender down at least once. Blend on medium speed for a few seconds. Let batter sit for 3 to 5 minutes.
Heat a nonstick saucepan over medium heat; when a drop of water sizzles, it is ready. Reduce heat slightly. Lightly brush the pan and a spatula with butter.
Stir the batter. Pour into a 1/4 cup measure and pour into the middle of the pan. Tilt the pan in a circular motion to spread the batter into 6- to 7-inch circle. Cook the crepe until the top looks dull and the edges brown, about 1 1/2 minutes. Work the spatula under the crepe; lift the edge. Grasp the crepe gently with the fingers of your other hand and lift it higher while sliding the spatula further under. Flip and cook 15 to 20 seconds more.