Boil pasta in salted water until al dente.
Heat a large skillet to medium-high heat. Add 1 tablespoon of olive oil. When the olive oil is hot, add 2 tablespoons of butter, melt.
In a bowl, mix 3 minced garlic cloves, red pepper flakes, lemon zest, salt and pepper. Add shrimp and coat.
Add the shrimp to the hot pan. Cook and flip shrimp for approximately 4-5 minutes or just until shrimp are curled and cooked through.
Remove shrimp and seasonings to a bowl. Set aside.
Melt 2 tablespoons butter in the same pan. Add 3 minced garlic cloves and saute 30 seconds.
Add the flour to make a roux and whisk together for 1 minute, then turn heat to low.
Slowly whisk in chicken broth, heavy cream and pesto. Continue whisking until the sauce is smooth.
Turn heat to medium high. Bring the sauce to a simmer. Heat approximately 3-5 minutes, stirring occasionally, until sauce is thickened.
Reduce heat to low. Add in lemon juice and Parmesan cheese until melted.
Add the shrimp with juices and pasta to the sauce. Stir until well coated in sauce.
Season with additional salt, pepper to taste.
Garnish with freshly grated Parmesan Cheese, fresh parsley and lemon juice.