Cover the eggplant meat with oil and salt. Place the eggplants and garlic head, meat side down, on a baking sheet covered with parchment paper. Remove garlic after cooking for 20 minutes. Cook the eggplants for 20 minutes longer (40 minutes total). Let cool for 10 minutes.
Scrape off the eggplant meat and place in a sieve, pressing gently to drain the liquid.
Place the eggplant meat, garlic head meat, mint, honey, oil, and lemon juice in a food processor and blend on low speed until the puree is smooth. Adjust seasoning. Let the mixture cool completely in the fridge.
When serving, drizzle with olive oil and sprinkle with za’atar. Serve baba ghanoush with raw vegetables.