In a medium sized pan, heat the olive oil over medium heat until hot. Add the garlic. Cook for 30 seconds or a minute until fragrant.
Add 1 tbsp of pesto into the garlic. Mix together then add the grape tomatoes. Cook, stirring occasionally, for about 3-4 minutes until tomatoes start to wilt.
Move the tomatoes to one side of the pan, and add the broccoli to the other. Season with salt and pepper. Add the rest of the pesto sauce to the broccoli and mix on "its side". Cover the pan and cook for about 5 minutes or until the broccoli has softened. Stir occasionally.
While the broccoli cooks, add the pasta to the pot of boiling water. Cook until al dente (about 8-9 minutes). Drain and set aside.
Once the broccoli is soft, mix the grape tomatoes and broccoli all together and add the sun-dried tomatoes, wine, and chicken broth. Bring to a boil and then lower heat. Cook, mixing frequently for about 3 minutes.
Add the pasta into the pan with vegetable, mixing frequently until you reach your desired texture.
Sprinkle the parmesan cheese into the dish, mixing frequently.
Serve hot and sprinkle with parmesan cheese to finish.