Heat a large pot over medium-high heat. Add turkey; cook and stir until browned and crumbly, 5 to 7 minutes. Add garlic, thyme, and black pepper. Add potatoes, cream of mushroom soup, onions, and water. Pour in enough chicken stock to cover potatoes. Reduce heat to medium-low; simmer soup until potatoes are tender, about 20 minutes.
Fill a blender halfway with the cooked onions and potatoes using a slotted spoon. Cover and hold lid down with a potholder; pulse briefly before leaving on to blend. Pour back into the pot. Repeat with any remaining onions and potatoes. Continue simmering soup until flavors are blended, 15 to 20 minutes more.