Place the wild rice and prepared bouillon in the Instant Pot. Pressure cook on High for 15 minutes. Quick release pressure. The rice should not be completely cooked, as it will be finished later in the recipe and you do not want it over cooked.
Drain the excess liquid from the rice. If you want to save Liquid to use when cooking the chicken that works nicely, if not no worries. Set the rice aside.
Set the Instant Pot to Sauté and add oil. Sauté the onions, until soft and translucent. Add carrots, celery and mushrooms. Saute for about another minute and turn off the Sauté function.
Add the chicken to the Instant Pot. Add enough water to reach the 10 -12 cup line. Larger chickens go to 12 cups, smaller go to the 10 cup line.
Pressure cook on High for 20 minutes. Quick Release the pressure.
Remove the chicken to cool and shred.
Turn the Sauté function back on and add the rice back to the pot.
Add the bouillon granules, white pepper and salt. Simmer for about 15 minutes. If you need to add more water do so at this time.
While the soup is simmering, in a medium saucepan melt butter on medium heat.
Whisk in the flour until smooth.
Slowly whisk in the milk and half and half. Continue cooking until bubbly and thick.
To keep the milk mixture from curdling or clumping, you cannot just add to the simmering pot quickly. Instead add about ¾ to 1 cup of the broth mixture to the milk mixture in the saucepan stirring well.
Add the milk mixture to the Instant Pot and mix well.
Add the shredded chicken and white wine. Heat through for about 10-15 minutes.