Cook pasta al dente according to package directions, in generously salted water. Add the broccoli just 1 minute before the pasta is finished cooking. Drain and set aside.
While the pasta is cooking, heat a large heavy-duty pan to high heat. Add the olive oil, butter, shrimp and garlic. Season with salt and pepper. Cook the shrimp on the highest heat level for 2-3 minutes or until pink. Remove shrimp from pan.
To the same pan, Whisk in flour until lightly browned, about 1 minute. Gradually whisk in milk, and cook, whisking constantly, until slightly thickened, about 1-2 minutes. Stir in cream cheese and parmesan and whisk until the cream cheese is fully mixed in and lump free. Taste and season with salt and pepper as needed.
Return the shrimp, drained pasta and broccoli to pan. Gently toss until everything is fully coated in the sauce. Turn off heat and serve hot.