In a large Dutch oven, heat 2 teaspoons olive oil over medium heat. Sauté the onions and garlic until softened, about 10 minutes. Remove from pan and set aside.
Heat the remaining oil over medium-high heat and brown the beef on all sides. Spoon the onions around the roast and pour in the coffee and broth. Add the salt, pepper, thyme and bay leaf. Bring to a boil and cover. Put the pot into oven and cook 1 hour and 40 minutes. Baste occasionally.
Remove the roast from pan and let rest 15 minutes.
Remove the onions from the pan with a slotted spoon and set aside. Discard the bay leaf; degrease the liquid.
Mash together the butter and flour.
Bring the liquid to a boil and slowly whisk in the butter mixture. Simmer the sauce 10 minutes; it should be slightly thickened. Stir in the onions and vinegar; check the seasonings.
Carve the roast thinly and serve with the onion sauce.