If using a grill or oven, preheat it to 450F. If using a gas stovetop, set it to a medium-low heat.

Poke the eggplants all over with the tip of a knife and place them onto the grill. If using an oven, place the eggplants onto a sheet pan lined with parchment paper. If using the stovetop, place the eggplants onto a wire rack and set it directly over the flame.

Cook the eggplants, flipping them 2 or three times, until blackened all over and very soft in the middle. Depending on the size of the eggplants, the entire process will take between 30 and 40 minutes total on a grill or in the oven. On a stovetop it will take between 15 and 20 minutes.

Transfer the eggplants to a wooden board and let them cool for a few minutes before peeling off the charred skin. Discard the tops of the eggplants and finely chop the flesh until it forms a smooth paste. Transfer the eggplant to a bowl along with the garlic and a pinch of salt. Mix thoroughly to combine and set aside at room temperature for at least 10 minutes. Discard any excess liquid.

Add the yogurt to the eggplant and mix well to combine. Taste for seasoning and adjust with salt or garlic as desired. Cover and refrigerate until ready to serve.

If using a grill, place the chile peppers and tomato onto the grill grates and cook, flipping once or twice, until just charred all over, around 5 minutes total. If using a stovetop, place the chile pepper and tomato onto a wire rack, place it directly over a medium flame and cook, turning often, until just charred all over, around 5 minutes total. Slice the chile into thirds and tomatoes into wedges. Transfer the vegetables to a plate and set aside until ready to serve.

Preheat a frying pan over medium heat. Add the olive oil and heat it until shimmering. Raise the heat to medium-high, add the ground lamb and cook, crumbling it into small pieces with a spatula, until browned, around 8 minutes. Add the red bell pepper, tomato paste, paprika, salt and pepper and cook, stirring until incorporated, around 2 minutes. Add the water and cook, lifting any brown bits off the bottom of the pan, until almost fully evaporated, around 3 minutes. Add the butter and cook, stirring, until melted, around 2 minutes. Remove the pan from the heat, taste the mixture for seasoning and adjust with salt and pepper as desired.

To serve, spread the reserved eggplant onto a platter and top with lamb mixture. Arrange the charred green chiles and tomatoes around the edge of the platter and garnish everything with sumac, red pepper flakes and parsley. Serve immediately with grilled flatbread or tortillas.