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Preheat the oven to 400°F. Get out two large baking sheets; there's no need to grease them. If you have parchment, get out two pieces of parchment.
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Whisk together the dry ingredients, then work in the butter until the mixture is crumbly.
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Add the grated cheese and stir until thoroughly combined.
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In a separate bowl whisk together the egg and vinegar until frothy, then add the water.
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Add the wet ingredients all at once to the dry ingredients, mixing to make a cohesive dough. Add additional water a teaspoon at a time, if necessary to bring the dough together.
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Divide the dough into two pieces, and shape each into a rough square.
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Roll out one piece of dough at a time, keeping the piece you're not working with covered to prevent drying.
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Lightly dust your work surface, or a piece of parchment, with gluten-free flour blend.
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Roll the dough 1/4" thick, and cut into 1" squares, use a pizza or pastry wheel, a bench knife, or a plain knife. Prick each cracker with a fork.
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If you've rolled on parchment, simply lift the parchment onto the baking sheet. Separate the crackers a bit, leaving about 1/4" between them, so they crisp evenly. If you're not using parchment, transfer the crackers to the baking sheet, leaving about 1/4" between them.
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Repeat with the remaining piece of dough.
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Bake the crackers for 12 to 16 minutes, until their edges are starting to brown.
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Remove them from the oven, and cool right on the pan.
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Store cooled crackers in an airtight container, or tightly wrapped in plastic.
