Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrots and celery; cook 5 minutes, stirring occasionally, until softened. Add the garlic and thyme and cook 1 minute more.
Stir in the rinsed wild rice blend and the chicken broth. Bring to a boil, then reduce the heat to low, cover, and simmer 35-40 minutes, until the rice is tender and the carrots are soft.
Stir in the shredded rotisserie chicken and simmer 2 minutes to warm through.
Whisk the cornstarch with 2 tbsp water, then whisk in the milk. Stir the mixture into the soup and simmer uncovered 3-5 minutes, until lightly thickened. Season with salt and pepper.
Ladle into bowls and serve hot. Leftovers keep refrigerated up to 4 days; reheat gently with a splash of broth.