In a Dutch oven, warm 1 tablespoon of olive oil over medium heat. Brown the lamb stew meat until it’s no longer pink, then remove with a slotted spoon and set aside.
Add onions, carrots, and the remaining olive oil to the pan. Cook for 5 minutes, stirring occasionally, until the onions are tender and aromatic.
Return the lamb to the pot along with the potatoes, beef broth, salt, and pepper. Bring everything to a boil.
Transfer the Dutch oven to a preheated 350°F oven. Cover and bake for 50 to 60 minutes or until the lamb and vegetables are fork-tender.
Using a slotted spoon, remove the meat and vegetables to a large bowl and keep them warm. Pour the pan juices into a separate bowl and set aside.
In the Dutch oven, melt the butter over medium heat. Stir in the flour, whisking until smooth.
Slowly add the reserved pan juices to the butter-flour mixture, whisking constantly. Bring to a boil and allow the mixture to thicken, which should take about 2 minutes.
Stir in the parsley, chives, and thyme. Return the lamb and vegetables to the pot and gently mix to coat everything in the gravy. Heat through before serving.