Combine the wild rice, mushrooms, chickpeas, onion flakes, garlic powder, poultry seasoning, thyme, rosemary, and pepper in the Instant Pot. Add the stock, vegetables, and salt.
Lock the lid into place, set the Pressure Release Knob to Sealing, select the Pressure Cook/Manual setting at high pressure, and set the cook time to 42 minutes. Once the cooking cycle is done, let the pressure release naturally.
Meanwhile, make the cashew cream by blending the ingredients on high for 5 minutes, or until smooth. Alternatively, substitute with 1 cup non-dairy cream.
Open the lid and stir in the cashew cream. Select the Sauté setting and simmer until thickened to your preference, 2 to 3 minutes. Taste for seasoning, adjusting if needed.
If you would like the soup a bit thinner, add more stock and let heat a few minutes. Select the Cancel setting. Serve the soup hot.