Bring a large pot of salted water to a rolling boil, then add the pasta and cook until al dente, about 8 minutes. Drain and set aside, reserving a cup of pasta water.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the wild shrimp, season with salt and pepper, and cook for about 2-3 minutes per side until pink and opaque. Remove from skillet and set aside.
In the same skillet, add a little more olive oil if needed, then sauté 2 cloves of minced garlic until fragrant, about 30 seconds, being careful not to burn it.
Meanwhile, in a blender or food processor, combine the basil leaves, toasted pine nuts, 2 cloves of garlic, Parmesan, lemon juice, and 1/3 cup olive oil. Blend until smooth and bright green, scraping down the sides as needed. Taste and adjust seasoning if necessary.
Return the cooked shrimp to the skillet, then add the pesto and stir to coat the shrimp evenly. If the sauce feels too thick, add a splash of the reserved pasta water to loosen it and create a silky texture. Cook for another minute to heat through.
Add the drained pasta to the skillet and toss gently to coat all the noodles in the pesto. If needed, add a little more pasta water to help the sauce cling to the pasta. Cook for 1-2 minutes until everything is heated through and well combined.
Finish by squeezing a little more lemon juice over the pasta and adjusting salt and pepper to taste. Serve immediately, garnished with extra basil leaves or grated Parmesan if desired.
