Cover the chicken tenders with cool water in a large pot or Dutch oven. Bring the water to a full boil over medium high heat and then turn the heat off under the pot.
Cover the pot and let the chicken sit in the hot water for 15 minutes undisturbed.
Remove the chicken from the pot and shred it, discarding any connective tissue or gristle. You may need to put the chicken tenders on a plate to cool enough to handle before you can shred the chicken.
Pour off and discard all but about two cups of the water that you cooked the chicken in.
While the chicken is cooking, in a large skillet, melt the 3 tablespoons of butter. Add the diced carrots and the diced celery, cooking them together and stirring with a spatula until the carrots and celery are soft.
Add the mushrooms and cook them along with the celery and carrots until the mushrooms are lightly golden.
Also, while the chicken and veggies are being cooked, you can prepare the wild rice mix. Simply follow the instructions on the box to make it in the microwave or on the stovetop. This should take about 20 to 25 minutes.
Next, add the broth to the pot in which you cooked the chicken along with the chicken cooking water.
Add the shredded chicken, cooked wild rice, and sauteed veggies. Stir in the thyme. Turn heat under the pot to low.
Using the same skillet in which you cooked the veggies, melt the 4 tablespoons of butter over medium high heat and then add the flour, stirring to combine.
Stir till the flour and butter are a light brown, stirring constantly.
Add the flour mixture to the soup pot, stirring it into the broth. Turn the heat back up under the pot and bring it to a low boil. Stir the soup; it should thicken slightly as you heat it.
Turn the heat down to a simmer. Add in the parsley and the half and half, stirring to combine. When the soup is steaming hot, serve it.
To store leftovers, allow the soup to come to room temperature before putting it into a container with an airtight lid and placing it in the refrigerator for up to 3 days. You can reheat leftovers in a bowl by microwaving it for about 2 minutes. Alternatively, you can use a saucepan over medium heat to warm the leftover soup.