Heat the olive oil in a 7-8-qt. pot over medium heat.
When the olive oil is fragrant, add the onion to the pot and season with ½ teaspoon of salt. Saute the onion for 8-10 minutes or until translucent.
Add the garlic and celery and saute for an additional 2-3 minutes.
Deglaze the pan with white wine and scrape any brown bits from the bottom of the pot.
Add the wild rice to the pot and toss with the other ingredients. Toast the wild rice for 3-4 minutes and then add in 5 cups of the vegetable broth. Bring to a boil.
Add the remaining salt, fresh thyme, and pepper. Cover and turn the heat to simmer. Cook for 40 minutes, stirring periodically.
After 40 minutes, check to ensure the wild rice has begun to pop or is al dente (it will continue to cook). If the wild rice is still very crunchy, simmer for another 15 minutes.
Remove the bundle of thyme. Add the pumpkin, coriander, cumin, paprika, white beans, and the remaining water to the pot and stir to combine. Bring to a simmer and cook for 15-20 minutes or until the rice reaches the desired consistency.*If you want the soup to be thinner, add 1-3 cups of water until it reaches the desired consistency.
Stir in the kale and cover. Let the kale cook down for 5 minutes.
Top the soup with roasted pepitas and serve.