1. Season and Brown the Lamb:

Season the lamb shoulder chops generously with salt and black pepper.

Heat the vegetable oil in a large, heavy skillet over high heat.

Working in batches, cook the lamb shoulder chops until browned on both sides, 3 to 5 minutes per side. Don’t overcrowd the pan.

Transfer the browned lamb chops to a stock pot or Dutch oven.

2. Sauté the Onions and Make the Roux:

Reduce the heat to medium. Add the chopped onion and a pinch of salt to the same skillet.

Cook and stir the onion until slightly softened and the edges are browning, about 5 minutes.

Stir in the butter until melted. Add the flour and stir until the onions are coated, about 1 minute. This creates a roux, which will thicken the stew.

3. Deglaze and Thicken:

Pour the chicken stock into the onion mixture. Bring to a boil, stirring constantly.

Add the dried rosemary. Continue to stir until the mixture thickens, 5 to 10 minutes.

4. Combine and Simmer:

Stir the chopped carrots and celery into the pot with the lamb shoulder chops.

Pour the thickened chicken stock mixture over the top.

Add water as needed to cover the meat completely.

Bring the mixture to a simmer. Then reduce the heat to low, cover the pot with a lid, and cook until the meat is almost falling off the bone, about 1 ½ hours.

5. Add Potatoes and Continue Simmering:

Transfer the meat to a plate using a slotted spoon.

Stir the potatoes into the stew. Return the meat to the stew, placing it on top of the vegetables.

Simmer, covered, until the potatoes are tender and the meat is falling off the bone, about 30 minutes.

6. Reduce and Thicken (Final Step):

Transfer the meat to a plate using a slotted spoon.

Bring the stew to a boil over medium-high heat. Cook, skimming off any fat that rises to the surface, until the stew is reduced and thickened, 10 to 12 minutes.

7. Shred and Return Meat:

Remove the meat from the bones. Discard the bones and any large pieces of fat.

Stir the shredded meat back into the stew.

8. Finish and Serve:

Stir in the chopped green onions. Season the stew with salt and pepper to taste.

Serve hot, and enjoy your hearty and flavorful Irish Stew!