Pat the ribs dry and season them generously with salt and pepper. In a small bowl, whisk together the balsamic vinegar, stock, and mustard.
Heat a very large skillet over medium-high heat, then add the ghee and swirl the pan to coat the bottom. Add the short ribs in a single layer, working in batches if your pan isn’t large enough, and sear until browned on all sides, 10-15 minutes total. Transfer the ribs to a slow cooker, arranging them vertically.
Add the onion to the pan and stir. Add the vinegar mixture and all the remaining ingredients, scraping the bottom of the pan using a spatula to dislodge any browned bits. Bring to a simmer, then pour everything into the slow cooker.
Cover and cook on high for 4 hours or on low for 7-8 hours, until the <g class="gr_ gr_95 gr-alert gr_gramm gr_disable_anim_appear Punctuation only-ins replaceWithoutSep" id="95" data-gr-id="95">meat</g> falls apart easily.
Use tongs to remove the ribs from the slow cooker. Serve hot over parsnip puree, with some onions and cooking liquid spooned on top.