In a large Dutch oven or heavy-bottomed pot over medium heat, cook the Italian sausage for 7 to 9 minutes, breaking it apart with a wooden spoon, until browned and fully cooked.
Using a slotted spoon, transfer the sausage to a plate. Leave the drippings in the pot.
Add 1 tablespoon of butter to the pot. Add the onion, carrots, and celery. Cook for 5 to 7 minutes, stirring occasionally, until the vegetables begin to soften.
Add the garlic and cook for about 30 seconds.
Stir in the rinsed wild rice, chicken broth, thyme, salt, and pepper.
Bring the mixture to a boil. Reduce the heat to low, cover, and simmer for 40 to 50 minutes, or until the wild rice is tender and the grains begin to split. Cooking time may vary depending on the wild rice.
Return the cooked sausage to the pot and stir to combine.
In a separate medium saucepan over medium heat, melt the remaining 3 tablespoons of butter. Whisk in the flour and cook for 1 to 2 minutes, whisking continuously, until smooth and lightly bubbling.
Gradually whisk in the heavy whipping cream until smooth. Slowly whisk in about 1 cup of hot broth from the soup pot. Continue cooking for 2 to 3 minutes, whisking, until the mixture is smooth and slightly thickened.
Slowly pour the cream mixture into the soup, stirring to combine.
Simmer uncovered for 5 to 8 minutes, stirring occasionally, until the soup thickens to your desired consistency.
Stir in the spinach and cook for 1 to 2 minutes, just until wilted.
If the soup is thicker than you would like, stir in additional chicken broth until it reaches your preferred consistency.
Garnish with fresh parsley, if desired, and serve warm.