Heat the oven to 450 degrees.
Place the halved bell peppers on a parchment-lined baking sheet, skin side up, and drizzle lightly with oil. Place the eggplants on a separate lined baking sheet. Transfer both baking sheets to the oven, setting the peppers on the top shelf. Roast the peppers for 25 to 30 minutes, until charred and softened, and the eggplants for about 50 minutes, until completely collapsed and softened through the middle.
Once cool enough to handle, peel and discard the skin of the peppers and finely chop the flesh; set aside.
Peel the eggplants, discarding the skins and stems, and place the flesh into a sieve set over a bowl. Leave to drain for at least 20 minutes, pushing down to squeeze out and discard any extra liquid. Roughly chop the eggplants.
Meanwhile, heat the ¼ cup oil in a medium skillet over medium-high. Once hot, add about three-quarters of the garlic plus the tomato paste, cumin, paprika and Aleppo pepper flakes; cook for about 1 minute, stirring occasionally, until fragrant. Add the blitzed tomatoes, parsley, cilantro, sugar and ¾ teaspoon salt. Bring to a simmer then turn the heat down to medium and cook for about 6 minutes, stirring occasionally, until slightly thickened and the oil has separated.
Add the chopped peppers and eggplants and cook, stirring, for 3 minutes. Off the heat, stir in 1 tablespoon lemon juice; set aside to cool slightly.
Meanwhile, make the tahini sauce: In a small bowl, whisk together the tahini with the remaining garlic, 1 tablespoon lemon juice, ⅛ teaspoon salt and 3 tablespoons water until easily pourable. Add a splash of more water if necessary.
Transfer the zaalouk to a wide, shallow bowl and drizzle with the tahini sauce. Sprinkle with extra Aleppo and cilantro and serve warm or at room temperature, with pitas to mop it all up.
