Begin by cutting the chicken breasts in half lengthwise to create thin cutlets, which will cook quickly and evenly. Season both sides generously with salt and pepper before dredging them lightly in flour, ensuring an even coating.

Heat a generous drizzle of olive oil in a large skillet over medium-high heat until shimmering. Add the floured chicken cutlets in a single layer, allowing them to sear undisturbed for 4-5 minutes until they turn golden brown, then flip and cook for another 4-5 minutes until fully cooked through.

In the same skillet, reduce heat to medium and add a tablespoon of butter. Once melted, add the sliced mushrooms with a sprinkle of Italian seasoning. Sauté for about 5-7 minutes, until browned and the liquid has evaporated.

Remove the sautéed mushrooms. In the same skillet, add another tablespoon of butter and minced garlic, cooking for about 30 seconds until fragrant. Pour in the chicken broth, lemon juice, and Dijon mustard, stir well, and let simmer for about 3-4 minutes.

Stir in the heavy cream, mixing well to create the sauce. Return the seared chicken and sautéed mushrooms back into the skillet, simmer together for an additional 5 minutes, adjusting seasoning with salt and pepper as necessary.