Heat the olive oil in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides.
Stir in the sliced leeks and minced garlic. Cook for 3 minutes until the leeks soften.
Pour in the chicken broth, then add the dried thyme, 1/2 teaspoon salt, and black pepper. Bring to a simmer and cook for 15 minutes.
While the stew simmers, boil the potatoes in a separate saucepan until tender. Drain and mash them in a mixing bowl.
Mix the mashed potatoes with the flour, egg, and remaining 1/2 teaspoon salt until a soft dough forms. Roll the dough into small balls.
Drop the dumplings into the simmering stew. Cover and cook for 10 minutes until the dumplings float and feel firm.
Stir in the heavy cream and heat through for 2 minutes. Adjust salt if needed before serving.