Season beef shanks with salt and pepper. In skillet, heat oil until smoking. Brown shanks on both sides; discard oil. Over medium heat in oiled skillet, saut (10 minutes) 4 sprigs thyme, bay leaf, smashed garlic clove, sliced carrot, chopped onion, sliced celery, and 2 cups cranberries.
Add beef stock; boil, simmer, and skim.
Place shanks and liquid in lidded pot; boil.
Bake (2 hours); remove shanks. In saut pan, melt butter.
Add 2 sprigs thyme and minced shallot; saut over medium heat (2 minutes).
Add dried cranberries and wild mushrooms. Saut (6 minutes); stir. Strain liquid into pan with mushrooms and dried berries. Simmer (4 minutes), turn off heat, and add chopped parsley. Pair with polenta.