Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Place the cheese, flour, everything bagel seasoning, salt and pepper in a food processor and pulse until combined. Add the butter and pulse until the mixture turns to small pea-size pieces. Continue pulsing and add the water, 1 tablespoon at a time, until the mixture resembles couscous and sticks together when you squeeze a small amount in your hand. Turn it onto a lightly floured surface and use your hands to work the mixture together into a ball of dough. Roll it out to 1/4 inch thickness and then cut out 1 1/2-inch squares. Place them 1 1/2 inches apart on your baking sheets, sprinkle with a bit more salt if you'd like and bake until they're lightly browned, about 20 minutes.