Season the chicken strips with Italian seasoning, salt, and pepper, and add them to the skillet; cook over medium heat for 7 to 8 minutes or until cooked through. Remove chicken from the skillet and set aside.
Combine heavy cream, chicken broth, and pesto in a mixing bowl; whisk until well combined and set aside.
Return the skillet to the heat and add the remaining olive oil; stir in the onions and cook for 2 minutes. Stir in garlic and sun-dried tomatoes; cook over medium-high heat for 30 seconds or until fragrant.
Add bell peppers and continue cooking for 4 minutes, or until fork tender.
Add the prepared pesto sauce to the skillet and bring to a simmer.
Return the chicken to the skillet and cook for 2 minutes or until heated through and the sauce is a little thickened. Taste for salt and pepper; adjust to taste.