In a small bowl, stir together the yogurt, minced garlic, lemon juice and salt. Use milk to thin the sauce to the desired consistency and set aside. The garlic flavor will become more noticeable the longer it sits with the yogurt.
Slice the eggplant in half lengthwise and sprinkle liberally with salt (you can slice the stem off first but I think it looks prettier attached, like poached pears). Place in a colander over the sink.
Preheat a grill to medium-high for 10-15 minutes.
Rinse the salt from the eggplant and lightly pat dry. Place in a large bowl and toss with just enough olive oil to prevent the eggplant from sticking to the grill.
It is easiest to grill the eggplant in batches since they are small and don’t take very long. Place 10-15 eggplant halves on the grill, flat side down. Cook for 2 minutes and then flip them carefully with tongs. Close the lid and cook for another 2 minutes. Remove from the grill, cover with foil to keep warm and repeat with the remaining eggplant.
Just before serving, drizzle the eggplant with the garlic yogurt sauce and sprinkle liberally with pomegranate seeds.