Cut the zucchini in half lengthwise, then slice into half moons. Slice the mushrooms and dice the roasted bell peppers.
Slice each chicken breast in half widthwise to create 2 thinner pieces. Pound lightly if necessary to ensure even thickness. Combine 1 tsp of Italian seasoning with salt and pepper (I add 1/2 tsp salt and 1/4 tsp pepper) and season one side of each chicken piece.
Heat the olive oil in a large, heavy-bottomed skillet over medium-high heat. When hot, add the chicken, seasoned side down. Season the other side with the remaining seasoning mixture. Cook undisturbed for about 4 minutes, then flip and continue cooking another 3–4 minutes or until chicken is golden brown and fully cooked (internal temperature should reach 165°F). Remove chicken from the skillet and cover with foil to keep warm.
Using the same skillet, add the butter, zucchini, and mushrooms. Cook for about 3–5 minutes or until crisp-tender, stirring occasionally. Add a tiny pinch of salt and pepper, then add the diced roasted red bell pepper, 1 tsp Italian seasoning, and minced garlic. Stir until fragrant, about 30 seconds; transfer the vegetables to a plate.
To the skillet, add 1/2 cup chicken broth and reduce heat to medium. Scrape the pan to release any browned bits and cook until the broth has reduced to about half, about 1 minute. Add remaining 1/2 cup broth, cream, remaining 1 tsp Italian seasoning, Dijon mustard, and Parmesan. Bring to a simmer, then reduce heat to medium and simmer for 2–3 minutes until thickened. Stir frequently. Stir through basil if using.
Taste sauce; adjust seasoning as needed. I love to add some fresh lemon. There are two options for serving: 1. Toss the cream sauce with freshly cooked pasta and some reserved pasta water until nicely emulsified, then add the chicken (diced or thinly sliced) and the cooked vegetables. 2. Or return the chicken and any accumulated juices to the skillet with the cream sauce, spoon the veggies around the chicken, and serve straight from the skillet. Garnish with additional freshly grated Parmesan if desired. Enjoy hot!
