Place brown rice flour in a resealable plastic bag. Add butter to the bag one cube at a time, shaking to coat each cube evenly with flour. Seal bag and place in the freezer for 15 minutes.

Whisk eggs and vinegar together in a small bowl. Place in the refrigerator.

Pour gluten-free flour into a large bowl. Cut in cold flour-coated butter cubes with your fingers until mixture resembles pebbles with some large lumps of butter remaining. Stir in egg and vinegar mixture. Mix in water, 1 tablespoon at a time, until dough is no longer sticky and forms a ball.

Wrap dough in plastic wrap; refrigerate until firm, about 30 minutes.

Divide dough into 2 pieces and roll out to desired thickness on a lightly floured work surface.