Rub bunch of green onions with ¼ tbsp olive oil. On a grill or in a grill pan over medium high heat, grill whole bunch of green onions turning occasionally until charred in parts, about 10 minutes. Remove and let cool 5 minutes. Add charred onions garlic, lemon juice, salt and pepper to a food processor. Pulse until chopped. Run adding remaining 1 TBSP olive oil 1 tsp at a time and process until fully incorporated and a thick paste* is formed. Set aside.
Cook pasta according to package directions, reserving ½ cup of pasta water before draining. In a large skillet over medium high heat, add chicken broth and Italian seasoning. Simmer 1 minute. Stir in charred green onion paste. Simmer additional minute. Add tomatoes and shrimp. Cook for 3 minutes. Add ½ cup of pasta water. Continue to cook for 1 minute, or until shrimp are pink. Stir in pasta. Remove from heat. Serve with grated Parmesan cheese.
* Extra olive oil can be added to make a marinade for flank or skirt steak, chicken, or fish. Good served over coconut rice.