Make linguine according to the instructions on the package. When cooked, drain and add back to the pot, cover and set aside.
In a food processor, combine basil, garlic, pinenuts, and parmesan cheese. Puree until combined. As the food processor continues to run, slowly drizzle in 1/2 cup olive oil. Season with salt and pepper to taste.
In a medium skillet over medium heat, warm 1 Tbsp olive oil. Add shrimp with a pinch of red pepper flakes. Cook until golden.
Add broth and lemon juice. Simmer for a couple of minutes until the shrimp is cooked through. Remove from heat and stir in parsley. Keep warm over low heat.
Stir in pesto into the pasta and toss to coat. Add in shrimp and toss everything together. Serve immediately.