With a chicken breast flat on a cutting board, using a sharp knife, about 1/3 of the way down the thick side, cut a deep pocket horizontally into the center of the meat about 3/4 of the way down, being careful not to cut through to the other side. (The pocket will be about 2 1/2 inches long and 1 1/2 to 2 inches deep.) Repeat with the remaining breasts. Wash hands well.
In a small bowl, mash together the goat cheese, butter, chives, parsley, thyme, lemon juice and garlic. Season with a pinch of salt and freshly ground black pepper. Divide into 4 equal pieces and form plugs to fit inside the chicken breasts. Insert 1 into each breast and press the edges of chicken meat to seal. Lightly season with salt and freshly ground black pepper.
In a large shallow bowl, combine the flour and the Essence. In another bowl, beat the egg with the water.
One at a time, lightly dust the chicken on both sides with the flour, then dip in the egg, shaking to remove any excess. Place again in the flour and turn to completely coat, shaking to remove any excess. Set aside.
In a large, oven-proof skillet, heat the oil over medium-high heat. Add the chicken and sear until golden brown, 2 to 3 minutes on each side. Place the pan in the oven and bake until the chicken is cooked through, 7 to 10 minutes.
Remove from the oven. Arrange the risotto in the center of 4 plates and place the chicken to the side. Arrange the carrots along the bottom of the plates, and garnish with parsley. Serve immediately.
In a medium saucepan, bring the stock to a simmer over medium heat. Reduce the heat to very low to keep hot.
In a large heavy saucepan, heat the oil and melt the butter over medium-high heat. Add the shallots and garlic, and cook, stirring until fragrant and soft, about 3 minutes. Add the mushrooms and cook, stirring, until wilted and their liquid is evaporated, 4 to 5 minutes. Add the rice and cook, stirring constantly, until the grains are opaque, about 1 minute. Stir in the thyme. Add the wine and cook, stirring, until nearly all evaporated. Add 3/4 cup of the stock, the salt, and pepper. Cook, stirring constantly, until the stock is nearly all evaporated. Continue adding more stock 1/2 cup at a time as the previous addition is nearly absorbed, until the rice is tender and the risotto is creamy, 18 to 20 minutes. Stir in cream, 1/2 cup of the cheese, and the parsley and mix well.
Remove from the heat and adjust the seasoning, to taste. If desired, stir in truffle oil to taste.
Serve immediately, topping each portion with a sprinkling of the remaining cheese and ham.
Homemade Chicken Stock:
In a large stockpot, combine all the ingredients and bring to a gentle boil. Reduce the heat and simmer, uncovered, for 2 hours, skimming the surface occasionally to remove any foam that forms on the surface.
Remove from the heat and strain through a fine mesh strainer into a clean container. (If necessary, strain again.) Remove the meat from the bones and reserve for another use. Discard the bones and vegetables. Let the stock cool completely, and refrigerate overnight. Skim any fat that forms on the surface. Keep refrigerated in airtight containers until ready to use, up to 3 days, or freeze for up to 2 months.
On a cutting board, using a sharp, heavy knife, cut the carrots in half crosswise, then in half lengthwise. With the flat edge down, cut into thin slices. Place the slices in a stack and slice into even matchstick pieces. (If a fine dice is required, these pieces in turn are chopped into equal small cubes.)
Bring a pot of salted water to a boil. Add the carrots and blanch until just tender, 1 to 2 minutes. Remove with a slotted spoon and shock in the prepared ice bath to stop cooking and preserve color.
When ready to serve the carrots, in a large skillet, melt the butter over medium-high heat. When foamy, add the carrots and cook, stirring, until warmed through and glossy, about 1 minute.
Remove from the heat, sprinkle with the parsley and serve immediately.