Prepare your meat and broth. In a pan over medium heat, melt butter and add the lamb leg, diced onion, turmeric, and black pepper.
Saute until the meat has browned and juices are bubbling, around 8-10 minutes.
Add 3 cups of water before covering and reducing heat to simmer (medium low) and cook for 20-25 minutes. Check close to 20 minutes to see if meat is tender– once it has reached that point, remove from heat.
Keep the remaining broth, more than 2 cups, in the pot to be used later.
While the meat is simmering, take the time to wash your peas. Rinse the peas through cold water and repeat this 3-4 times.
In a small saucepan, add the peas and enough water to cover the peas by an inch. Bring the water to a low boil and cook for 5 minutes, adding a pinch of salt before the boil. Note that you do not want to cook the peas all the way here, as they will lose their shape later in the cooking this way. Instead, cook until they are slightly softer but still too firm to eat.
After 5 minutes, drain the peas and set aside.
Prepare your fried onions. In a separate large skillet, heat vegetable oil and fry the sliced onions. They should be golden brown and slightly crispy. Mix in the tomato paste and fry for another 2 minutes. Add the split peas, crushed limoo amani, and the advieh. Set to medium-low and sautee for 8-10 minute, stirring often.
Prepare your whole limes while the mixture is sauteeing. Pierce a hole through the lime and set into hot water for about 4 minutes before using. This will help the flavors of the lime infuse with the stew.
Into the large skillet, add the broth and lamb. Add a pinch of salt and stir ingredients together. Add your 2 prepared limes and move heat to low.
Cover the skillet with a lid and simmer for 40 minutes, until everything is tender.
While the Gheymeh is cooking, cook your potato wedges.
Slice into inch long sticks and rinse under cold water. This will rid the potatoes of their starch.
In a large skillet over medium-high heat, heat 4 tbsp olive oil. Pat dries the potatoes and toss into heated oil. Toss to coat and fry for 12 minutes.
Remove the fries from oil and let excess oil drop off on a rack and paper towel. Sprinkle salt onto fresh fries.
Serve the Gheymeh on top of aromatic rice, with potato wedges on top of it all. Enjoy!