In a food processor, combine basil, slivered almonds, garlic, lemon zest, lemon juice, and Parmesan cheese. Pulse until finely minced, then slowly add olive oil while blending until smooth.
Bring a large pot of salted water to a boil. Cook spaghetti according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the pasta.
In the same pot, heat olive oil over medium heat. Add shrimp and cook for 2-3 minutes on each side until pink and opaque. Avoid overcooking.
Add the drained spaghetti back to the pot with shrimp. Pour in reserved pasta water and stir to combine.
Stir in the pesto sauce until pasta is thoroughly coated. Serve immediately, garnished with fresh basil or extra Parmesan if desired.
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Notes
Store leftovers in an airtight container in the fridge for 3 to 4 days. Reheat gently, adding a splash of water if needed.