Season the beef on both sides with salt and pepper. In a large skillet, heat the oil until it is almost smoking. Add the roast and sear on each side until brown, about 4 minutes per side. Place the roast in the bottom of the slow cooker.
Add the onion and carrot to the oil remaining in the skillet. Saute over medium heat for about 5 minutes. Add the garlic and saute about a minute longer, just until fragrant. Pour 1 cup of broth into the saute pan and scrape up any bits that might be stuck to the pan. Pour the stock and the vegetables over the top of the roast in the crockpot.
Only if necessary, add more water, so that the water will be at least halfway of the side of the roast. (I did not need any additional liquid.)
Cover and cook on low for 6 hours or on high for 4 hours. I cooked mine for about 4 1/2 hours on high and it was absolutely falling apart. I then turned the crockpot to warm for another hour or so to wait until we were ready to eat.
When ready to eat, remove the bones and the roast from the crockpot. With an immersion blender, puree the liquid remaining in the crockpot to use for gravy. (You could also do this in a blender.) I only had about a cup or so of liquid, but was able to easily puree it by tipping the crockpot slightly to the side. Season the gravy with salt as needed. Enjoy!