Begin by cutting the chicken breasts in half lengthwise to create four thinner cutlets. Season both sides generously with salt and pepper, then dredge each cutlet in flour, shaking off any excess.

In a large skillet, heat olive oil over medium-high heat. Once the oil is shimmering, add the seasoned chicken cutlets to the skillet. Sear each side for about 4-5 minutes, or until golden brown and cooked through. Remove the chicken from the skillet and place it on a plate to rest.

In the same skillet, reduce the heat to medium and add butter. Once melted, add the sliced mushrooms along with Italian seasoning. Stir occasionally until mushrooms are tender and have released their moisture, about 5-7 minutes. Remove from the skillet and set aside.

Add minced garlic to the skillet and sauté for about 1 minute. Pour in chicken broth, stirring in lemon juice and Dijon mustard. Bring to a simmer and let it reduce by half, around 3-4 minutes.

Reduce heat to low and stir in heavy cream until well combined. Return the seared chicken and sautéed mushrooms to the skillet. Cook for an additional 5 minutes, adjusting seasoning with salt and pepper to taste.