Set the Instant Pot to Sauté and heat the olive oil. Add the diced onion and cook, stirring, until softened, about 2–3 minutes.
Add the cumin, cinnamon, and nutmeg to the onions and cook, stirring, until fragrant, about 1 minute.
Meanwhile, place the chicken broth and sliced dates in a large microwave-safe bowl and heat until the broth is very hot, about 1–1½ minutes.
Transfer the hot broth and dates to a food processor and process until the dates are mostly broken down with only a few small pieces remaining.
Add the tahini, lemon juice, and salt to the processed broth and dates and blend until smooth and combined.
Season the chicken breasts with the za'atar and place them in the bottom of the Instant Pot on top of the onions.
Pour the tahini-date sauce over the chicken, close the lid, set the valve to sealing, and cook on Manual/High pressure for 10 minutes.
When the cook time finishes, perform an immediate (quick) pressure release. Carefully remove the chicken to a cutting board.
Switch the Instant Pot to Sauté and cook the sauce, stirring frequently, until it thickens, about 5–10 minutes.
Shred or slice the chicken, return it to the pot, and stir to coat with the thickened sauce.
Garnish with chopped cilantro and mint and drizzle with honey if using, then serve.
