Add chuck roast, 1 cup beef broth, 1/4 cup balsamic vinegar, onion, garlic cloves, soy sauce, honey, dried rosemary, salt, and pepper into a 6 quart crock pot. Place a lid on top then cook on low for 7-8 hours or until meat shreds easily. Shred meat then return to crock pot and cook on low for 1 more hour.
Meanwhile bring remaining 1 cup balsamic vinegar to a boil in a small saucepan then turn heat down to medium and simmer until vinegar is thickened and slightly sweet tasting, about 20 minutes. You'll know it's done when you scrape a spatula across the bottom and the vinegar stays parted for a second or two. Pour reduced balsamic vinegar into a serving dish. (Can do this ahead of time - microwave reduced balsamic vinegar for 15-20 seconds to get it to pouring consistency.)
Strain the cooking liquid from the crock pot through a fine mesh sieve lined with cheese cloth into the same saucepan, leaving a little bit of liquid in the crock pot to keep the meat juicy. Put the meat back into the crock pot and place a lid on top to keep warm. Add remaining beef broth to the saucepan then bring mixture to a boil and then turn heat down to medium and simmer until reduced and vinegar taste has mellowed, 20 minutes. Pour the au jus into a serving dish.
Heat oil in a medium-sized skillet over medium-high heat. Add half the shallots then saute, stirring occasionally, until golden brown, 2 minutes. Transfer to a paper-towel lined plate to drain then sprinkle lightly with salt and repeat with remaining shallots.
Pile meat onto buns then top with crispy shallots, blue cheese, and reduced balsamic vinegar. Serve with au jus on the side.