Preheat oven broiler.
In a small bowl, combine half of the lemon zest, half of the dried dill and all of the cream; set aside.
Cook spaghetti for 3 minutes less than stated in package directions, stirring occasionally; add artichoke hearts and roasted red peppers and cook until heated through about 2 minutes.
Reserve 1 cup of pasta cooking water then drain pasta and vegetables in a colander over another bowl or saucepan. DO NOT DISCARD WATER. Return water to a saucepan and bring to a boil. Add cubed flounder; cook for 4 to 5 minutes or just until fish turns opaque and flakes easily when tested with a fork.
Carefully remove fish from water with a slotted spoon; set aside and keep warm, now discarding water.
Add pasta/veggie mixture, half and half mixture, lemon juice, salt, pepper and remaining lemon zest and dill to the saucepan; cook and toss over medium heat for 1 minute or until pasta is al dente and well coated. If mixture seems dry, add a few tablespoons of water and cook until heated through.
Arrange evenly on dinner plates and top with flounder. Sprinkle each serving with Parmesan.