Slice each chicken breast in half lengthwise to make four thinner chicken breast cutlets. Season both sides with salt, black pepper, and paprika, before transferring them to a large bag filled with 3 tablespoons of all-purpose flour. Dredge to coat.
Heat a large, heavy-bottomed pan or skillet over medium-high heat. Add the olive oil plus 1 tablespoon of butter.
Once the pan is hot, add the chicken, gently shaking to remove any excess flour before adding to the skillet. Sear the chicken for approximately 3-5 minutes on each side, or until golden and nearly cooked through. Remove chicken and transfer to a clean plate. Set aside.
In the same skillet over medium heat, melt the remaining butter and add the mushrooms. Cook the mushrooms until golden and they start to release their water. Season with Italian seasoning and add the minced garlic. Continue to cook, stirring often, until most of the water has evaporated (cooked off).
Remove the mushrooms to a clean plate or the same plate as the chicken. Deglaze the skillet with a splash of white wine (optional) or lemon juice. Scrape up any stuck-on brown bits.
Add the chicken broth and bring to a low boil. Reduce heat to low and add the heavy cream and grated parmesan cheese. Mix well to combine. Return the chicken and mushrooms back to the pan and allow everything to cook, altogether, for 3-4 minutes, or until heated through and the creamy mushroom sauce has thickened.
Season with additional salt and pepper, if needed, and garnish with fresh thyme if desired. Enjoy!