Begin by heating 1 tablespoon of olive oil in a large, 12-inch nonstick skillet over medium heat.

Season the chicken strips with Italian seasoning, salt, and black pepper. Place the seasoned chicken in the skillet and cook for approximately 7 to 8 minutes, or until the chicken is thoroughly cooked. Once done, remove the chicken from the skillet and set it aside.

In a small mixing bowl, combine the heavy cream, chicken broth, and basil pesto. Whisk these ingredients together until the mixture is well blended. Set aside.

Return the skillet to the stove and add the remaining 1 tablespoon of olive oil. Add the diced onions to the skillet and sauté for about 2 minutes. Following the onions, incorporate the minced garlic and chopped sun-dried tomatoes into the skillet, cooking for an additional 30 seconds over medium-high heat, or until the mixture becomes fragrant.

Introduce the sliced bell peppers to the skillet, continuing to cook for approximately 4 minutes, or until the peppers are tender to the fork.

Pour the previously prepared pesto sauce mixture into the skillet, and bring to a simmer, allowing the flavors to combine.

Add the previously cooked chicken back into the skillet, simmering for an additional 2 minutes to ensure the chicken is heated through and the sauce slightly thickens. Season with additional salt and pepper according to taste.

To serve, garnish the dish with freshly grated Parmesan cheese and chopped basil. This dish can be served alone or accompanied by a side of pasta, rice, or crusty bread to enhance the meal.