Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain.
Season chicken pieces with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Brown chicken until cooked through, approximately 5 to 7 minutes. Remove chicken and set aside.
In the same skillet, sauté minced garlic for 1 minute. Add sun-dried tomatoes, oregano, and red pepper flakes, stirring for another minute.
Pour in heavy cream and chicken broth. Bring to a simmer over medium heat for 3 to 5 minutes until the sauce begins to thicken.
Whisk in the grated Parmesan cheese until melted and the sauce is smooth.
Return the cooked chicken and pasta to the skillet. Toss thoroughly to coat. Incorporate reserved pasta water as needed to reach desired sauce consistency.
Garnish with julienned basil and serve immediately.