Julienne all the vegetables. Boil the pasta until it's firm, 1 minute less than the cooking time on the package.
Add some vegetable oil (not listed) to a frying pan and stir fry the vegetables. When they're more or less cooked, push them to the sides of the pan.
Turn the heat down to low. Add the ketchup and mirin to the center of the pan. Spread it out thinly with a spatula, and wait until it's bubbling all over. (Don't let it burn.)
When the moisture in the ketchup has reduced to about half, add the cooked spaghetti. Turn the heat up to high and stir-fry. Season with salt, pepper and butter.
Sprinkle parsley and grated cheese on top, and serve.
Story Behind this Recipe
Pasta napolitan is the one dish my husband makes better than I do!
If you reduce the ketchup while heating, the pasta will be nice and separated instead of sticky. Taste and add more ketchup if needed. The butter is added at the very end for some flavor only. You can use bacon instead of ham!