Heat the vegetable oil in a large pot or Dutch oven over medium heat. Add the lamb or mutton chunks and brown them on all sides. Remove the meat from the pot and set it aside.
In the same pot, add the onions and garlic. Sauté until they become translucent and fragrant.
Sprinkle the flour over the onions and garlic, stirring well to coat. This will help thicken the stew later on.
Add the tomato paste and stir it into the mixture until well combined.
Return the lamb or mutton to the pot, along with any juices that accumulated. Add the potatoes, carrots, celery, and thyme leaves. Season with salt and pepper to taste.
Pour in the beef or vegetable broth, making sure all the ingredients are submerged. If needed, add additional water to cover the ingredients.
Bring the stew to a boil, then reduce the heat to low and let it simmer for about 1.5 to 2 hours, or until the lamb is tender and the flavors have melded together. Remember to stir occasionally to prevent sticking.
Taste and adjust the seasoning as needed. You can add more salt, pepper, or thyme to taste.
Once the stew is done, remove it from the heat and let it rest for a few minutes before serving. This will allow the flavors to settle.
Serve the Irish stew hot, preferably with some crusty bread on the side. Enjoy!
