In a large Dutch oven, heat 2 tablespoons olive oil over medium-high heat. Season the lamb shanks with salt and pepper. Add them to the pan and sear each side until golden brown, 5–7 minutes per side. Remove shanks from the pan and set aside.
Lower heat to medium. Add the shallot and 1 tablespoon fresh thyme (or 1 teaspoon dried) to pan. Sauté until shallot is translucent, 1–2 minutes. Add the mustard to the pan and stir well.
Sprinkle the flour over the mustard, then stir until all of the flour is absorbed.
Slowly pour the stout into the mustard-flour mixture, whisking to dissolve the flour into the liquid. Add 1 cup water.
Return shanks to the pan and bring liquid to a simmer. Cover and reduce heat to maintain a gentle simmer. Turn shanks every 15 minutes, until the lamb is falling off of the bone, 1½ hours to 1 hour 45 minutes. (If the shanks stick to the bottom, reduce heat slightly.) While shanks cook, prepare the vegetables.
Preheat oven to 400°.
In a medium mixing bowl, combine 1 tablespoon olive oil and lemon juice and toss in the potatoes and carrots. Add 1 teaspoon fresh thyme (or ½ teaspoon dried). Season with salt and pepper.
Arrange the carrots and potatoes in a single layer on a 10- by 15-inch lined, rimmed baking sheet. Roast, stirring occasionally, until they begin to brown and are easily pierced with a fork, 40 to 45 minutes.
To serve, defat the lamb cooking liquid, divide potatoes and carrots between two warm shallow bowls and top with shanks. Drizzle with gravy and sprinkle with lemon zest. Serves 2 as a main course.
***Estimated cost for 2 servings: $19.71, or $9.86 per serving.
This recipe is easily doubled: Simply add another two lamb shanks to the mix and be sure that braising liquid reaches halfway up the side of the shanks, adding more water if needed. Then braise as instructed. Double the amounts for the potatoes and carrots too.
Read the story:: Cooking Fresh on a Budget: Lamb