For the yogurt sauce, combine the first 7 ingredients in a medium bowl and stir well, adding more or less liquid to create the desired consistency (start with a little less if you prefer it thick). Set aside; you want the garlic especially to settle into the yogurt base.

Arrange the eggplant and pepper on the pan for the broiler. Make diagonal slices in the flesh of the eggplant to increase absorbency. Drizzle with olive oil and sprinkle a bit of salt over both, and broil cut-side up for 5 minutes, until the eggplant flesh is browning. Turn and cook another 5 minutes, so that the skin of the eggplant and peppers have blistered and browned.

When ready to serve, drizzle the vegetables with sauce and garnish with roughly chopped fresh parsley.