Heat 1/2 tablespoon olive oil in a 4- to 5-quart Dutch oven set over medium-high heat until it shimmers. Add half of the lamb, and brown on all sides, 7 to 8 minutes total. Remove the lamb to a bowl and repeat with the remaining oil and lamb. Remove the second batch of lamb to the bowl and add the carrots to the pot. Saute the carrots for 3 to 4 minutes, stirring occasionally. Return all of the lamb to the pot along with the grits and stir to combine. Add the chicken broth and bring to a boil. Once boiling, decrease the heat to low, cover, and simmer until the liquid is absorbed and the lamb and grits are tender, 30 to 45 minutes. Just before the stew is finished, add the oregano. Taste for seasoning, and add salt and pepper as desired. Serve in bowls.