Melt butter with olive oil in a large pot over medium heat.
Add onions, celery, and carrots. Season with salt, pepper, and thyme. Cook until softened.
Add garlic and cook for 1 minute until fragrant.
Sprinkle in flour and stir continuously for 2 minutes.
Slowly add chicken broth while stirring. Increase heat to medium-high.
Add heavy cream, cooked chicken, and seasoning packet from the rice.
Bring to a boil, then reduce to simmer. Stir occasionally for 10 minutes.
Stir in cooked wild rice and soy sauce.
Simmer for another 10-15 minutes until thickened and creamy.