Start preheating the oven to 350F.
If you like garlic and want to add a couple of full heads, it's a creamy deliciousness once cooked, do as follows. Remove as much loose skin as you can. Cut off about a quarter to one third from one end. Garlic heads will go in the braising pan later, while some of the cut off pieces can be used in this recipe in place of the two required garlic cloves and the rest can be saved for other uses.
Heat the olive oil with two tablespoons of butter in a braising pan over medium-high heat. Add the beef and brown on all sides. Remove the meat from the braising pan and set aside.
Add the onions, mushrooms, shallots, carrots and leeks. Saute until the vegetables are slightly softened, about 4-5 minutes. Add the minced garlic and continue sauteing for another minute.
Add the remaining two tablespoons of butter and let it melt, while constantly stirring. Turn the heat down to low. Have the broth ready. Add the flour and stir briskly until it is fully incorporated. Pour in the broth, turn the heat up to medium high and let the liquid mixture come up to a boil. Reduce heat to medium and simmer, constantly stirring, until the mixture starts to thicken. It shouldn't take long, less than a minute. Remove from heat.
Add the pepper and nutmeg, stir, then salt to taste. Stir in the red wine vinegar. The sauce may taste a little too tart right after you add the vinegar, but it will be perfect by the time it's done cooking.
Nestle beef pieces and garlic heads, if using, in the sauce, spreading them out evenly. If using, place the garlic bulbs cut side up. Garlic smell can be quite strong, so add those bulbs only if you love garlic and have a good ventilation in the kitchen. If you place it cut side down, the sauce will get infused with garlic too much.
Cover and braise in the oven at 350F for 3-4 hours. I think the beef only gets better if cooked a little longer.
Serve with freshly made mashed potatoes, garnish with chopped fresh herbs, and enjoy.