In a large mixing bowl or stand mixer, combine Greek yogurt and flour until a thick dough forms. If dough is too dry, add a little water until dough comes together; set aside.
In a large pot, melt butter over medium-high heat. Add onion, carrots and celery and cook for 5 minutes, or until vegetables are tender. Add garlic and cook for an additional minute.
Sprinkle flour on top, stir to combine and cook for 1 minute. Add evaporated milk and chicken stock and stir to combine. Bring to a boil then add cooked chicken, thyme, salt and pepper.
Reduce heat to low, then carefully drop 1 Tablespoon size dough pieces into the soup. Press dough down into the soup until fully submerged.
Cover pot and simmer for 20 minutes, or until dumplings are cooked through (they will still have a soft consistency) and serve.