In a large pot of boiling salted water, cook pasta according to package directions. Save 1 cup pasta water. Drain and set aside.
In a large skillet over medium high heat, heat oil and butter.
Season shrimp with salt and pepper and place in skillet. Cook for 3 minutes a side and remove to a plate.
In the same skillet, add garlic and anchovies. Stir around unil the anchovies break up and the garlic is fragrant. This will take literally 1 minute. DO NOT let the garlic burn.
Add in tomatoes, olives, capers and red pepper flakes. Stir to combine. Allow to simmer for 5-10 minutes.
Add back in shrimp and pasta. Combine and check to see thickness of sauce. If too thick add in 1/4 cup reserved pasta water and see if you need to add more water to get the thickness you desire.
Serve with grated Parmesean cheese and basil.