In a pot add enough water to generously cover the chicken breasts. Add the salt. Bring to a boil bring to a boil and cook until chicken is tender, about 25 minutes.
Remove chicken and allow to cool enough to handle. Cut into bite-sized pieces.
Return the chicken to the pot and reserve 6 cups of the boiled chicken stock (water). Add the butter and the cream to the broth. Cook over medium heat cook, stirring occasionally, for a couple of minutes. Stir in the chicken. Cook over for about 20 minutes, stirring occasionally.
Meanwhile, in a mixing bowl add the flour and baking powder, stir well Add the oil and buttermilk and begin stirring until it forms a soft dough (like the consistency of pie dough). Knead over about 4 - 5 times. Pinch off into balls (any size you prefer) and drop into the broth.
Let the dumplings cook for about 5 minutes, stirring occasionally
Dissolve the cornstarch in the cold water and stir into the broth. Continue stirring the soup until it thickens slightly, about 3-5 minutes. Season, to taste. Serve warm.