Add the olive oil to the pot of the Instant Pot and press the Saute function. Once the oil is warm, add the leeks, shallot, and celery and cook until softened and translucent, about 5 minutes. Add the garlic, mushrooms, thyme and salt, and cook until mushrooms are just beginning to soften, about 3 minutes.
Add the wild rice and vegetable broth. Lock the lid of the Instant Pot and place the pressure release handle in the Sealing position. Cook for 45 minutes on Manual / High Pressure. When the rice is done cooking, release the steam.
Fold the kale and goat cheese into the pot. The rice will continue to absorb the liquid as it sets.
Taste and adjust the seasoning if desired. Leftovers are great for up to 4 days in the refrigerator, or freeze for up to 6 months.