In a wide dutch oven, heat 3 tablespoons olive oil at medium-high, until shimmering. Add ⅓ of the sliced onions and saute until light golden brown and crisp, about 10 to 15 minutes. Using a slotted spoon transfer the onions to a plate. Tip: Add a pinch of salt when the onions are half cooked.

In the same dutch oven, add the cherry tomatoes and sear on all sides until edges are dark brown. Transfer the tomatoes to the same plate with fried onions.

Add the remaining sliced onions to the dutch oven and saute until translucent, about 5 minutes. Then add grated garlic and stir until aromatic, about 1 minute.

Push the sautéed onions to the edge of the pot or transfer to a plate. Drizzle more olive oil if needed. Arrange the lamb meat pieces in a single layer and raise the heat to high. Quickly sear the meat on both sides at high heat, until golden brown, about 3 minutes each side.Tip: It is important to brown the meat only on the surface and don't cook the inside.

Add advieh, turmeric, black pepper and salt. Stir to combine with meat and sautéed onions. Then add some water, tomato sauce, dried limes, saffron water (if using) and stir well.

Raise the heat and bring the mixture to a boil. Cover with a lid, lower the heat and simmer, until meat is 80 percent done, stirring in between, about 1¼ to 1½ hours (time will vary).

While the stew is simmering, prepare the eggplant. Preheat oven to 425 ºF.

If using large globe eggplants (American variety), cut the eggplant into halves and then cut ½ inch thick slices. Brush eggplant slices with 2 to 3 tablespoons olive oil on both sides.

Arrange the slices on a parchment paper lined baking sheet and bake until fork tender, about 25 minutes (time may vary with oven). See notes for skillet fried eggplant.

Cut the roasted eggplant slices in the center if they are too large. Add the roasted eggplant and lime juice to the dutch oven and continue to simmer until the eggplants are soft and tender, about 30 minutes.

The sauce will thicken and some oil will trickle to the surface. Meat should easily fall off the bone. Taste and adjust the seasonings. Top with fried onions and seared cherry tomatoes and cook another 10 minutes. Serve khoresh bademjan hot with Persian saffron rice and tahdig.