Yes this can be made Dairy free by replacing sharp cheddar with Daiya Cheese.  You can also use different variety of cheeses such as mozzarella.

2 tbsp butter (or earth balance dairy free butter) ~ 1 large egg ~ 1/2 tsp salt ~ 1/8 tsp pepper ~ 2 cups grated sharp cheddar or cheese of choice ~ 3/4 cup rice flour ~ 1/4 cup potato starch ~ 1/4 tsp xanthan gum ~ extra salt for sprinkling

Beat the butter until cream. add egg, salt and pepper and beat until blended. Beat in cheese until combined and then stir in flours and gum until well blended.  Work dough into a ball.  If the dough don’t stick add cold water 1 tbsp at a time.  divide into balls and roll as thin as possible.  sprinkle with salt and cut into squares or use a gold-fish cookie cutter.   bake at 350 degrees until deep golden brown.

Warning, addictive, very addictive.