Preheat the oven to 475 degrees . On a baking sheet, toss the green beans, shallots, garlic and olive oil; season with salt and pepper. Roast until the green beans are crispy on the edges, 10 to 12 minutes.
While the green beans are cooking, butterfly the chicken by slicing horizontally into the thick, long side of each breast, being careful not to slice all the way through; open like a book. Using a mallet, pound each chicken breast out a bit. Season with salt and pepper. Top each chicken breast with the sliced garlic, lemon zest, soft cheese, layers of herbs and greens and the shaved Parm. Roll up each bundle and tie with 3 pieces of kitchen string ; season.
Heat a cast-iron skillet over medium-high. Add the oil, two turns of the pan. Add the chicken and cook, turning, until evenly browned, about 6 minutes.
Remove the green beans from the oven and reduce the heat to 400 degrees . Add the chicken in the skillet and roast until cooked through, 8 to 10 minutes. Transfer the chicken to a cutting board. Place the skillet back on the stove; add the wine and stock. Cook over medium heat, whisking up the browned bits, until the sauce is reduced slightly, about 2 minutes. Swirl in the lemon juice and the butter.
Cut the strings off the chicken; slice each into 1/2-inch-thick pinwheels. Arrange the chicken on plates and top with the lemony pan sauce. Serve the green beans alongside the chicken.