Reduce the heat to medium and pour in the red wine, scraping up any browned bits from the bottom of the pan.
Add the beef broth—just enough so the liquid reaches at least halfway up the sides of the roast. The amount needed will vary depending on the size of your pot. For a 3.5-quart braiser, 2 cups of broth is typically needed.
Tie the rosemary and thyme together with kitchen twine to create an herb bouquet, then submerge it in the liquid. Add the bay leaves and the whole head of garlic. Bring the mixture to a steady simmer—not boiling, but a gentle, consistent simmer over medium-low heat.
Cover and cook until the roast is fall-apart tender, about 3.5 to 4 hours. Check the roast every hour, adding more broth if needed to keep it at least halfway submerged. I typically don’t need to add more, but it depends on how quickly your liquid reduces.