Boil the Artichokes: Bring the water, bay leaves, salt, and peppercorns to a boil in a large pot.
With a small, sharp knife, trim the tough outer skin from the artichoke stems and remove the bottom row of leaves. Using long handled tongs, carefully add the artichokes and lemons to the pot and return to a boil. Place 2 small heavy plates on top of the artichokes to keep them submerged, lower the heat, and cook at a low boil until the artichokes are tender, 20 to 25 minutes. Drain in a colander and let the artichokes sit until cool enough to handle.
Pull off the large outer leaves from the artichokes, and discard or reserve for another use. Remove and discard the spiky inner leaves. Scrape the hairy choke from each heart and cut into 1/4 inch thick slices. Set aside to use in sauce.
Make the Chicken and Sauce: Preheat the oven to 350 degrees F. Line a baking sheet with aluminum foil and set aside.
Season each chicken breast half with 1/2 teaspoon of the Essence and set aside.
Combine 1/2 cup of the flour with 1 1/2 teaspoons of the Essence in a shallow bowl. In another shallow bowl, combine the bread crumbs with the remaining tablespoon Essence. Put the egg wash in a third bowl.
Dredge the chicken first in the flour, shaking to remove any excess, then in the egg wash, letting any excess drip off, and then in the bread crumbs.
Heat the oil and melt 1 tablespoon of the butter in a large skillet or saute pan over medium-high heat. Add the chicken in 2 batches and cook until golden brown, 1 1/2 to 2 minutes per side. Transfer the chicken to the prepared baking sheet and roast until cooked through, 15 to 18 minutes.
Meanwhile, in a large clean skillet, heat 2 tablespoons of the remaining butter over medium-high heat. Add the yellow onions and cook, stirring, until soft, about 3 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Add the mushrooms and cook until soft and they give off their liquid, about 4 minutes. Add the salt and pepper and stir. Add the remaining 2 tablespoons flour, stir to incorporate, and cook until the mixture is thick, about 1 minute. Add the wine and cook, stirring, until evaporated, 30 seconds to 1 minute. Add the chicken stock, stir well to incorporate, and simmer until the mixture is thickened, about 2 minutes. Add the cream, bring to a simmer, and cook until the mixture is thickened enough to coat the back of a spoon, about 2 minutes. Add the sliced artichoke hearts and lemon juice and stir to incorporate. Remove from the heat and stir in the remaining tablespoon butter, the green onions, and parsley. Adjust the seasoning, to taste.
To serve, place 1 chicken breast in the center of each of four large plates and top each with an equal portion of the sauce. Serve immediately.