Preheat oven to 450°. Rub the eggplant, pepper and garlic with 1 tablespoon olive oil. Place these in a pan and roast for 20–25 minutes, until the vegetables are soft and the skin is beginning to brown.
Remove garlic cloves, broil on low for 7-10 minutes, flipping a couple of times to blister the skin of the vegetables. Remove from the oven and allow to cool for a few minutes and then remove the skin, seeds and stem from the pepper, the skin from the eggplant and the skin from the garlic.
Place the eggplant (about 1½ cups), pepper, garlic, remaining 2 tablespoons of olive oil, lemon juice, salt, thyme, date syrup and tahini in a blender. Blend on high until smooth. Serve warm or at room temperature with pita or fresh vegetables.