In a small bowl, combine the rosemary, sage, and thyme and stir to combine. Set aside.
To cut a chicken breast into a cutlet, start by placing the breast flat on a cutting board. Hold it steady with one hand, and with a sharp knife, slice horizontally through the middle of the breast, starting from the thicker side, until you have two thinner pieces. Place the chicken breasts on a cutting board and cover with parchment paper or plastic wrap. Using a meat mallet or the bottom of a heavy skillet, pound the chicken until it is a uniform ½-inch thickness. Pat dry with paper towels.
Season both sides of the chicken with salt, pepper and a dash of cayenne. Place flour in a shallow bowl. Place each piece of chicken in the flour and dredge of both sides, shaking off the excess flour. Set aside. Continue until all chicken is dredged in the flour. Reserve the additional flour in the bowl as you’ll need a bit of it for the roux.
Heat the oil in a large, deep skillet (or braiser) over medium heat. Working in batches, add the chicken and cook until golden brown on both sides, about 3 minutes per side. The chicken doesn’t have to be fully cooked through as it will finish in the sauce. Transfer the browned chicken to a plate and set aside and continue until all of the chicken is browned.
Reduce the heat to medium-low. Add the butter and garlic and cook, stirring, allowing the butter to melt and the garlic to toast slightly, being careful not to burn. Sprinkle in the reserved flour and stir to combine. Cook, stirring, toasting the flour so that it is lightly browned but being careful not to burn, about 2 minutes.
While stirring, add the white wine and stir, scraping up any browned bits. Add the broth and the herb mixture and continue to whisk until well combined. Increase the heat to medium and bring to a simmer and let cook, simmering and whisking often, until the broth begins to slightly thicken, about 4 minutes.
Reduce the heat so that it is lightly simmering (You don’t want a rapid simmer, but a nice steady simmer, about medium-low heat) and nestle the chicken into the sauce. Cover and cook until the chicken is cooked through, about 10 minutes.
Reduce the heat to low and carefully stir in the lemon juice. Taste the gravy and add a pinch more of salt, if desired. Garnish with a tiny bit of fresh parsley, if desired.