Cook pasta according to package directions. When pasta is ready, drain in a colander and rinse with cold water, reserving 1 cup of the pasta cooking water. Transfer pasta to a large bowl.
Spray a large, non-stick skillet with an olive oil mister or non-fat cooking spray and set over medium-high heat. Season shrimp with a bit of salt and pepper, then add into pan and cook until shrimp are pink and cooked through. Place shrimp in a bowl with pasta.
Re-spray the skillet with the non-fat cooking spray, add in tomatoes and garlic, and cook until tomatoes are slightly tender about 2 minutes.
Add in broccoli and cook for another 2 minutes.
Next, add in the goat cheese and 1/2 cup of the reserved pasta water and stir to combine until you have a creamy consistency. Add more of the reserved water if needed to achieve desired consistency.
Pour tomato, broccoli, and goat cheese mixture over pasta and shrimp. Add in fresh basil leaves. Toss to combine, and season with additional salt and pepper as desired. Serve immediately.