In a large pot, heat the vegetable oil over medium heat. Add the finely chopped onion and minced garlic, and sauté until golden brown.
Add the chicken pieces to the pot and brown them on all sides.
Add the chopped carrot, celery, sweet potato, white potato, pumpkin (or butternut squash), and corn to the pot. Stir to combine.
Add the green peas, diced tomatoes, fresh thyme leaves, chopped parsley, and bay leaves.
Pour in the chicken broth and bring the mixture to a boil. Reduce the heat to low and let it simmer for about 1-1.5 hours, or until the chicken and vegetables are tender.
In a mixing bowl, combine the all-purpose flour and salt.
Gradually add cold water to the flour mixture, mixing until a dough forms. If the dough is too dry, add more water, a little at a time, until the desired consistency is reached.
Pinch off small pieces of the dough and roll them into small balls or cylindrical shapes.
Gently drop the dumplings into the simmering soup. Cover the pot and cook for an additional 15-20 minutes, or until the dumplings are cooked through and tender.
Season the soup with salt and pepper to taste. Remove the bay leaves.
Enjoy your meal!