Cook pasta according to package. Drain and set aside.
In large skillet, melt 2 tablespoons butter and the olive oil over medium heat.
Brown chicken breasts on both sides until nicely golden and cooked through, about 8-9 minutes each side. Remove from pan and cut into 1/2 pieces.
Pour out drippings from pan but don't wipe the pan out. In the same pan, melt 1/4 cup butter on medium heat. Add the garlic and sun-dried tomatoes. Sauté for 2 minutes. Stir in heavy cream and dash of white pepper. Cook 5-6 minutes, stirring frequently. Slowly stir in the parmesan cheese into a creamy mixture, stirring constantly. Stir in the pesto sauce and cook for about 5 minutes, until thickened. Stir in the chicken pieces for about 3 minutes.
Serve with breadsticks.
Serve chicken and sauce over the hot noodles.
Garnish with parmesan cheese and fresh ground black pepper (optional).