Heat 1 tablespoon of olive oil in a Dutch oven over medium heat. Add the lamb and cook, turning occasionally, until browned on all sides and no longer pink in the center. Use a slotted spoon to transfer the seared meat to a bowl; set it aside.

Pour the remaining tablespoon of oil into the same pot and add the onions and carrots. Sauté for about 5 minutes, stirring occasionally, until the onions begin to soften and turn golden at the edges.

Return the lamb to the pot and add the cubed potatoes. Pour in the beef broth, then season the mixture with salt and pepper. Stir everything together, bring the stew to a rolling boil, then remove from heat.

Cover the Dutch oven with a lid and place it in a preheated 350°F oven. Bake for 50 to 60 minutes, or until the lamb and vegetables are tender enough to pierce easily with a fork.

Once the stew is cooked, use a slotted spoon to transfer the meat and vegetables to a large bowl and keep warm. Carefully pour the remaining juices from the pot into a separate bowl and set aside.

In the now-empty Dutch oven, melt the butter over medium heat. Stir in the flour and cook, whisking constantly, until a smooth roux forms. Slowly pour in the reserved pan juices while whisking to prevent lumps. Bring the mixture to a boil and stir continuously for about 2 minutes, or until the gravy thickens.

Add the parsley, chives, and thyme, then return the lamb and vegetables to the pot. Stir to combine, allowing everything to warm through before serving.