Add basil, pine nuts, cheese, garlic, and salt to the blender and pour remaining olive oil over the top.
Pulse several times to begin to blend. Scrape sides of the blender and pulse a few more times. You may need to scrape the sides again and pulse a few more times until all ingredients are well blended.
Set aside until ready to mic into pasta.
Shrimp and Pasta:
Cook shrimp while pasta is cooking.
Cook pasta according to the box instructions and before draining off water, set aside about a cup of cooking water. (Some cooking water will go into pasta and set aside extra just in case you will need to reheat the pasta leftover's later.)
Toss shrimp in a mixing bowl with salt, pepper, pressed garlic cloves, and grated Parmesan cheese until evenly coated.
Preheat a large cooking pan over medium-high heat for a few minutes and add oil.
Sear shrimp for about 2 minutes on each side, until they turn completely opaque. (Exact time will depend on the size of shrimp.) Take the shrimp out of the pan as soon as they are cooked.
Toss cooked pasta with pesto and about 1/2-2/3 cup of cooking water.
You can mix the shrimp right into the pasta or simple add it to the top of pasta.
Garnish with some shaved Parmesan cheese and pine nuts and serve!