Clean fish removing scales with a small knife. Try not hurting their flesh, since red mullets have a thin skin and can easily be damaged. Once cleaned inside out, rinse with running water.
Put Horio Koroneiki variety olive oil in a large pan (large enough for the fish) over medium heat. Add garlic and celery and cook for a few minutes.
Add some parsley and mix softly for 30-40 seconds. Then, add tomatoes, mix and leave for some seconds. Sprinkle with salt -not too much, since we can add more later- and pepper, reduce heat and cook for 15 minutes.
If liquid is evaporated, add a glass of water, because we need it slightly thin so that it covers the fish. When sauce is ready, add the fish – check to see if more salt is necessary beforehand.
Cover pan with a lid and cook for 15 minutes without turning fish from the other side. Slightly stir pan if necessary.
Cook for another 10 minutes and remove fish from the pan to a platter.
Add cooked spaghetti in the pan and mix well.
Serve spaghetti with sauce, topped with the fish and sprinkled with parsley.