In a liquid measuring cup place the apricot preserves, pomegranate vinegar and molasses, olive oil, mustard and garlic. Whisk together with a fork until well incorporated.
Pour half of the mixture into a slow cooker and place the turkey breast on top. Season turkey well with salt and pepper and drizzle the remaining preserve-vinegar mixture onto it. Sprinkle with za'atar spice. Cover, and cook on high for 31/2 to 4 hours or on low for 8 to 10 hours.
Taste for seasoning and adjust accordingly. Pull the meat using two forks and place on a serving platter. Sprinkle it with more za'atar and pomegranate seeds.