Bring a large pot of water to a boil. Add the pasta and cook according to the package directions until al dente. Reserve 1 cup of the pasta water and drain pasta in a colander and rinse with cold water. Set aside.
Add 2 tbsp of olive oil to a large skillet over medium high heat. Sprinkle the shrimp with salt and pepper and the zest and juice of 1 lemon. Transfer the seasoned shrimp to the hot oil and cook, 2 minutes on each side, until pink and fully cooked. Remove the shrimp from the skillet once cooked and set aside.
Place the remaining 2 tbsp of olive oil back into the skillet over medium high heat. Add the onion and tomatoes and sauté for 2-3 minutes until translucent and the tomatoes are slightly cooked.
Add the garlic and cook for 30 seconds. Add the broccoli and sauté for 2-3 minutes until bright green. Add 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 ensure a creamy consistency. Add the cooked pasta and the cooked shrimp and toss to combine.
Season with salt and pepper and serve immediately.