Preheat oven to 350, toast walnuts on rimmed baking sheet, tossing once, until golden brown - about 8-10 minutes.
Let toasted walnuts cool.
In a food processor, coarsely chop walnuts, garlic, cheese, and Za'atar.
With motor running, stream in olive oil, process until desired consistency is achieved. Salt to taste.
Place currants in a small bowl and cover with very hot water. Let sit until soft and plump, about 5-10 minutes.
Meanwhile whisk yogurt, lemon juice, and oil in a large bowl, add salt & pepper to taste. Thin with water until the consistency is that of heavy cream.
Drain the currants and add to the dressing along with the cabbage, carrots, and parsley. Salt to taste.
Add pesto to a platter and smear to distribute. Place slaw on top and sprinkle Za'atar on top of slaw.