Chill bowl and paddle of kitchen aide standing mixer.
Dissolve salt and sugar into water. Place in fridge.
Toss butter pieces in flour and coat each side. With the mixer on low, cut butter into flour. Pour water into mixer all at once. Increase speed to medium and mix until a dough is formed.
Divide dough into 8 parts, form into discs and wrap each in plastic wrap. Chill for 30 minutes.
Roll dough 1/8 inch thick. Trim dough into 4 inch rounds. Place dough rounds on top of greased balls of aluminum foil covered with parchment paper.
Brush with egg wash (1 egg beaten with 1 teaspoon of water.) Using some of the dough scraps, make a small ball and place on top of the round to create the top of a cloche.
Place balls on parchment lined sheet pans and place the dough scraps on a second sheet pan.
Bake at 400 until golden, about 20 minutes. Let cool, and carefully remove the dome from the ball.
In an 8-quart pressure cooker, heat 3 tablespoons canola oil. Saute half the onions, carrots, and celery with half the thyme, rosemary and sage for 15 minutes.
Season with salt and pepper.
Pour in 2 quarts chicken stock, add chicken breasts.
Bring the stock to a simmer and place lid on pressure cooker.
Cook for 30 minutes and remove from heat. Allow pot to cool before opening lid. Run cold water on the top if need be.
Remove breasts and set aside. Strain the broth into the large rondeau with the other vegetables and place the vegetables onto a sheet pan to cool. Remove the herbs.
When the chicken meat is cool enough to handle, tear it into bite size pieces. Set aside.
In the meantime, heat 3 tablespoons canola oil in another large rondeau.
Saute the other half of the onions, carrots, and celery with the other half of the thyme, rosemary and sage for 15 minutes. Season with salt and pepper.
Pour in 2 quarts chicken stock, add chicken bones from carcasses, wings and dark meat (legs and thighs).
Bring to a boil, then simmer for 90 minutes. Strain.
Note: Remove dark meat when meat starts to pull away from the bones, about 45 minutes. Set aside. When the meat is cool enough to handle, tear it into bite-size pieces. Combine with the breast meat.
In same pot, melt butter then whisk in flour until smooth. slowly whisk in the hot stock. Bring to a boil then simmer. Mixture should be the consistency of heavy cream. Stir in heavy cream.
Bring to a boil again, then simmer. Adjust seasoning with salt and pepper, if necessary.
In a medium size pot, combine the pulled chicken pieces, vegetables and enough sauce to generously coat the veggies. Reheat until hot, then stir in peas.
Place dough scraps in the bottom of individual bowls. Spoon chicken mixture on top, then ladle more sauce, if necessary. Top with the dough cloche. Place the fried herbs and roasted carrots on the side of each dish. Sprinkle the rim with the pea salt.