Position your oven rack about 6 inches from the broiler element and preheat the broiler to high. Line a baking sheet with aluminum foil.

Pierce each 2 large eggplants about 1 lb each several times all over with a fork (this prevents bursting). Place them directly on the foil-lined baking sheet.

Broil the 2 large eggplants about 1 lb each for 30–40 minutes, turning them every 10 minutes with tongs, until the skin is deeply charred and blackened on all sides and the 2 large eggplants about 1 lb each have completely collapsed and feel very soft when pressed.

Transfer the charred 2 large eggplants about 1 lb each to a colander set over the sink. Once cool enough to handle (about 10 minutes), split each 2 large eggplants about 1 lb each open lengthwise and scoop out the flesh with a spoon, discarding the charred skin. Let the flesh drain in the colander for 5–10 minutes — this removes excess liquid and prevents a watery dip.

Roughly chop the drained large eggplants about 1 lb each flesh on a cutting board with a knife, then transfer it to a mixing bowl.

Add the 3 cloves garlic minced or pressed into a paste minced, 3 tbsp tahini well-stirred, 3 tbsp fresh lemon juice from about 1–2 lemons, 2 tbsp extra-virgin olive oil, ½ tsp kosher salt, and ¼ tsp ground cumin to the mixing bowl. Mix vigorously with a fork until everything is combined and the dip is creamy but still has some texture. Taste and adjust: add more 3 tbsp fresh lemon juice from about 1–2 lemons for brightness, more 3 tbsp tahini well-stirred for richness, or more ½ tsp kosher salt as needed.

Transfer the baba ganoush to a wide, shallow serving mixing bowl. Use the back of a spoon to create swoops and swirls across the surface. Drizzle generously with 2 tbsp extra-virgin olive oil, then scatter chopped fresh flat-leaf parsley finely chopped, ¼ tsp smoked paprika, and 1 pinch sumac (if using) over the top.

Serve immediately with warm pita bread and fresh vegetables, or cover and refrigerate for up to 5 days.