In a soup pot, heat 2 tablespoons of the oil. Season the turkey legs with salt and pepper, add them to the pot and cook over high heat until browned on all sides, about 7 minutes. Add the water, stock, garlic, chopped celery, carrot, yellow onion, bay leaf, thyme sprig and peppercorns and bring to a boil. Cover and simmer over moderately low heat until the turkey legs are tender and the meat pulls away from the bone, about 1 hour.
Transfer the turkey legs to a large plate and let cool slightly. Pull the meat off the bones and coarsely chop it; discard the skin. Return the bones to the pot and simmer the turkey stock for 1 hour longer.
Meanwhile, in a medium skillet, heat the remaining 1 tablespoon of oil. Add the diced celery and red onion and cook over moderate heat until softened, about 5 minutes; transfer to a food processor. Add the turkey, season with salt and pepper and pulse until the turkey is finely chopped.
On a work surface, lay out 10 wonton wrappers. Scoop 1 tablespoon of the turkey filling into the center of each wrapper. Moisten the edges of the wrapper with water and fold it in half on the diagonal, creating a triangle; press the edges to seal. Transfer the wonton to a baking sheet and keep covered with a damp cloth. Repeat with the remaining wrappers and filling.
Strain the turkey stock into another pot and skim the fat from the surface. Season with salt and pepper and bring the stock to a simmer. Add the wonton, cover and cook until the wrappers are just tender, about 5 minutes. Ladle the soup into bowls, garnish with the dill and serve.