Place basil, garlic, Parmesan, pine nuts, and tomato in a food processor. Gradually add olive oil, while pulsing, until mixture is smooth and creamy.
In a bowl, stir together chicken broth, 1 cup white wine, dried basil, oregano, and minced garlic. Stir in chicken pieces.
Bring a large pot of lightly salted water to a boil. Add pasta, and cook until just al dente, about 8 minutes. Drain, and rinse under cold water. Toss with 2 tablespoons olive oil. Set aside.
Heat 3 tablespoons olive oil in a skillet over medium heat. Stir in onions, and sprinkle with sugar. Cook until the onions are soft and translucent. Stir in sun-dried tomatoes and pine nuts, and cook about 3 minutes. Stir in chicken and marinade. Stir in 1/2 cup white wine. Simmer chicken pieces, stirring occasionally, about 8 minutes.
Add pasta and pesto to the skillet. Stir in cream, and cook until the sauce is thickened. Adjust salt and freshly ground pepper to taste, and serve with freshly grated Parmesan.