Place the cocotte on the stove and heat half of the oil.
Season the beef shanks with salt and pepper. Flour the meat on both sides and sear on the hot oil.
Mince one of the shallots and add it, together with the pealed cloves of garlic, to the pan. Turn the meat over to sear on the other side.
Peel the carrots and chop them transversally into about 1/2 inch thick slices. Chop the onion. Peel the remaining shallots.
Pour the remaining olive oil in the pan. Add the onion, carrots and whole shallots and cook on medium heat until the onions are translucent, about 10 minutes. Season to taste with some sea salt.
Peel and chop the tomatoes and add them to the pan. Add the sprigs of thyme, the bay leaves and two lemon strips. Cook for about 5 minutes, then add the wine and 1 cup of water.
Cover and simmer for 2 hours. Then remove the lid and add the pimentón. Cook on low heat for about 25 minutes, or until the liquid reduces a bit.
To serve, place a portion of beef shank over a bed of mashed potatoes, then top with the carrots and shallots and some of the sauce.