Here are a few "test" crosshatching brushes. Some are fairly effective, but use these as guides for making your own since they're only captured brushes. Maybe some crosshatching experts will develop the approach further, which is what these test brushes are really about.
The assorted brush variants are directional. The "Angle" setting changes the angle of the form the hatching defines. Since most brushes are curved or offset, use directional strokes. Changing "Squeeze" will distort some of the curved nibs. Finally, the Mondrian variant isn't really a hatching brush, but it's kind of fun and it sure reminded me of the style. Have fun.
IMPORTANT: Be sure to make a backup of your "Pre-built Brush File." These brushes will quickly create a 200 mb Pre-built Brush File, so you may want to move the backup to a safe location and let Painter make a new one. In fact, captured brushes are so memory intensive that variants may load slowly or incorrectly. If you have limited disk space or RAM, "Insufficient Memory" errors can happen as well. Last but not least, changing brush settings like size will cause Painter to recalculate the brush. That can be time consuming.