Whisk broth, honey, balsamic vinegar, Bragg, shallot, salt, pepper, Worcestershire, and red pepper flakes in a medium bowl. Set aside.
Add oil to large skillet. Sprinkle roast with salt and pepper. Sear the roast on all sides and add to a slow cooker.
Add reserved liquid to slow cooker; add the garlic, thyme, and bay leaves.
Cook on low 5 hours. Remove from slow cooker and reserve liquids. Let stand at room temperature 5 minutes before slicing.
Melt butter in medium skillet. Add mushrooms. Cook 10 minutes.
While mushrooms are cooking, remove 2 cups of liquid and pass through a cheesecloth, several coffee filters, or a fat separator. Set aside.
Serve sliced roast with cooked mushrooms; top with strained liquid.