In a small bowl, whisk together 2/3 cup olive oil, garlic, salt, pepper, lemon zest, and lemon juice. Set aside.
Bring a large pot of salted water to a boil over high heat. Cook angel hair pasta according to the instructions on the box.
While the pasta is cooking, heat 1 tsp olive oil over medium-high heat. Season the shrimp with salt and pepper, then add to the skillet to cook, turning at least once. Remove from heat once shrimp turn pink, approximately 2 minutes.
Strain pasta when finished cooking and add it back to the large pot. Stir in lemon sauce, shrimp, chopped artichokes, basil and parmesan.
Serve immediately with grilled lemon halves, chopped basil and grated parmesan.