In a large pot, add the chicken broth, potatoes, and onions. Bring to a boil. Reduced heat, cover, and simmer for 10 minutes.
Stir in frozen vegetables and break up the frozen pieces, if necessary. Add the chicken, thyme, salt, and pepper. Bring back to a boil, reduce heat, and cover. Simmer for 5 minutes.
In a separate small bowl, add cornstarch or flour. Gradually add milk, stirring with a whisk, until well blended. Keep mixing until the cornstarch or flour is completely dissolved.
Increase the soup heat to medium. Using a rubber spatula or wooden soup, so you don’t smash the potatoes, stir in milk/cornstarch mixture. Continue to cook, uncovered, for about 5 minutes, to thicken. Stir often using the rubber spatula or wooden spoon. If it starts to boil, turn heat down to simmer.