Preheat the oven to 400°F. Line a baking sheet with foil.
Prick the eggplant all over with the tip of a sharp knife and place on the baking sheet. Cut the top off the garlic head, exposing the cloves. Rub the olive oil onto the cloves, then wrap the head in a square of foil. Set on the baking sheet.
Roast for 1 hour, turning the eggplant halfway through. After 1 hour, remove the garlic. Turn the eggplant again and continue cooking for 15-20 minutes, until very soft. Let cool until easily handled.
Slice eggplant down the middle and scoop out flesh into a sieve set over a bowl or the sink. Let drain 30 minutes.
Scoop the eggplant into a food processor. Squeeze the roasted garlic cloves from the skin and add to the processor, along with the yogurt and spices. Blend until completely smooth.
Taste and adjust seasoning. To serve, spread into a shallow bowl and sprinkle with extra smoked paprika and chopped parsley.
Notes
Makes about 1 ½ cups.
Store in an airtight container in the refrigerator for up to 3 days.