In a large pot, bring 16-20 cups water (4-5 quarts) to a rolling boil.
Add 1 - 1 ½ T sea salt and the dry pasta and cook 2 minutes LESS than the instructions on the label.
While the water is boiling and pasta is cooking, let’s make the sauce! In a large saucepan, heat EVOO and Butter on medium heat for 2-3 minutes.
Add minced shallot and cook for 2 minutes; then add garlic and heat an additional minute.
Add vegetable broth (or water) and let evaporate by heating for 2 minutes.
Add tomato paste and gently whisk to combine.
Whisk in cream and salt, increasing heat to med-high, and bring to a low boil.
Reduce heat to medium-low and cook for 5-6 minutes, stirring occasionally.
Whisk in lemon juice until incorporated; then remove from heat and whisk in parmesan cheese.
Once pasta is ready, reserve ½ cup of the pasta water. Then drain the pasta.
Add pasta to tomato cream sauce, with ¼ cup of the reserved pasta water
Gently toss to combine, and cook 2 minutes until gigli pasta is coated with sauce and fully cooked. If needed, add the remaining ¼ cup reserved pasta water
Buon Appetito!