Start by prepping the veggies: half the zucchini lengthwise and then slice into half-moons. Slice the mushrooms. Dice the roasted bell peppers.
Next, prep the chicken breasts: Remove excess fat and cut the large breasts evenly in half widthwise to get 4 thin breasts. Pound the breasts to make sure they are completely even thickness. Generously salt and pepper both sides of the breasts. Sprinkle 1 teaspoon Italian seasoning evenly among the breasts and rub into the breasts. Take each piece of chicken and dredge in the 1/3 cup of flour until completely coated. Set aside for a couple minutes to allow the chicken to come to room temperature.
Meanwhile, in a large nonstick skillet over low heat, melt 2 tablespoons butter. Add in the minced garlic and stir until fragrant, about 30 seconds. Add in the chicken broth and increase the heat to medium. Bring to a boil. Reduce the heat and simmer (uncovered) for about 5 minutes. Add in the heavy cream and 1 teaspoon Italian seasoning and bring to a boil while stirring. Simmer over medium heat until the sauce is just thick enough to coat the back of a wooden spoon.
While the sauce is simmering, grab another large skillet and place over medium high heat. Add in the oil and allow to heat until shimmering. Add in the chopped zucchini and sliced mushrooms. Cook, stirring occasionally until crisp tender. Add in the chopped roasted red bell pepper and last remaining teaspoon of Italian seasoning. Stir and then transfer to a plate.
In the same saucepan used to cook the veggies, add in the remaining 2 tablespoons butter. Once the butter is melted, add the prepared chicken breasts into the skillet. Cook over medium heat for about 3-4 minutes per side or until the chicken reaches an internal temperature of 165 degrees F.
Add the veggies and sauce in with the chicken and season additionally to taste with salt and pepper. Add in the fresh chopped basil.
If desired serve over cooked pasta with a generous sprinkle of Parmesan cheese.