Heat oven to 225°F. Slice each tomato lengthwise into 4 equal slices. Spread in single layer on two 15 x 10 x 1-inch jelly-roll pans. Sprinkle with sugar and vinegar.
Bake in 225 °F oven until tomatoes are dried, but still pulpy, about 2-1/2 hours, turning slices over after first hour (you should have about 3 cups).
Bring large pot salted water to boiling for cooking penne. In large skillet, heat oil over medium-high heat. Add chicken and garlic; sauté until chicken is just cooked through, about 5 minutes. Remove chicken to a plate.
In same skillet, combine wine, broth, cream, oven-dried tomatoes, salt and pepper flakes; simmer until slightly thickened, about 8 minutes.
Meanwhile, cook penne in boiling water until firm but tender, following package directions. For last 2 minutes of cooking, add broccoli; drain. Place penne with broccoli in serving bowl.
Add chicken to cream sauce; heat through, about 1 minute. Toss chicken and sauce with penne.