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1
Cook, drain and toss the spaghetti with butter, cheese, and parsley. Make sure the pasta is cooked al dente--more underdone--as it will continue to cook in later stages.
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2
Put the olive oil and onion into a small saucepan and turn the heat to medium. Cook and stir the onion until it becomes colored a golden brown, then add the cut-up drained tomatoes and salt. Cook for about 20 minutes until the oil floats free of the tomato. Take off the heat.
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3
When the tomatoes have cooled, mix in the diced mozzarella. Tip the pan and spoon off most of the oil.
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4
Add the tossed sauced spaghetti, salt and a few grindings of pepper to the beaten egg, mixing thoroughly to distribute the egg evenly over the pasta. Put the 1 tablespoon butter in a skillet, turn the heat on to medium and when the butter foam begins to subside, but before it darkens, but in just half the pasta and egg mixture, spreading it uniformly over the bottom of the pan. Over it, pour the tomato and mozzarella from the saucepan, spreading it evenly, and stopping a little short of the frittata's edge. Pour in the remaining half of the spaghetti and egg mixture and cover the frittata in the pan, spreading it out to the edges. Cook the frittata on top of the stove for 3 to 4 minutes without touching the pan. Then tilt the plan slightly bringing its edge closer to the flame of the burner. Keep the pan in this position for about 1 minute, then rotate it a shade less than a full quarter turn, always keeping it tilted so that its edge is close to the flame. Repeat the procedure until you have come full circle. Take a look at the underside of the frittata, lifting the edge gently with a spatula, to make sure it has formed a fine, golden crust all around; if it has not, cook a little longer where needed.
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5
Run the pan under the broiler until the top has formed a lightly colored crust. When ready, loosen the frittata with a spatula, slide it onto a platter, and cut it into serving wedges, like a pie.
