2 medium eggplants (about 1 pound each)
2 tablespoons olive oil, divided
1 teaspoon coarse or kosher salt, or to taste
6 tablespoons tahini (sesame seed paste), well-stirred if a new container
2 garlic cloves, peeled and minced or pressed
Juice of 1 lemon, plus more to taste, if desired
Pinch of cayenne or aleppo pepper
Pinch or two of ground cumin
2 tablespoons well-chopped flat-leaf parsley, divided
Toasted sesame seeds or za’atar for garnish