Cut the chicken breasts in half lengthwise to create four thinner cutlets. Season both sides with salt and pepper. Dredge each piece in flour.
Heat the olive oil in a skillet over medium-high heat. Cook the chicken cutlets for about 4-5 minutes on each side until golden brown. Remove chicken and set aside.
In the same skillet, add the butter, let it melt, then add the sliced mushrooms and Italian seasoning. Cook until mushrooms release moisture and become seared, about 4-5 minutes. Remove mushrooms and set aside.
In the same pan, add minced garlic, chicken broth, lemon juice, and Dijon mustard. Stir until the mustard dissolves. Allow to reduce by half for about 3-4 minutes.
Add heavy cream to the pan and stir. Return cooked chicken and mushrooms to the skillet. Cook for an additional 5 minutes or until the chicken is fully cooked and sauce has thickened. Season to taste.