Cut the chicken breasts in half lengthwise to create four thinner cutlets. Season them with salt and pepper, then coat them in flour.
Heat the olive oil in a skillet over medium-high heat.
Once the pan is hot, add the chicken and cook for 4-5 minutes per side, until golden brown. Once done, remove the chicken from the skillet and set it aside.
Add the butter to the pan and let it melt. Then, add the mushrooms and Italian seasoning. Cook the mushrooms, stirring occasionally, until they release their moisture, cook off the liquid, and develop a nice sear.
Remove the mushrooms from the pan (you can place them on the same plate as the chicken).
Add the garlic, chicken broth, lemon juice, and Dijon mustard to the pan. Stir well until the mustard dissolves, and let the mixture reduce by half, about 3-4 minutes.
Stir in the cream, then return the chicken and mushrooms to the pan. Let it simmer for another 5 minutes until the chicken is cooked through and the sauce thickens slightly. Season with salt and pepper to taste.