If using uncooked spaghetti, bring a large pot of salted water to a boil. Cook the spaghetti according to the package directions until al dente, approximately 8 to 10 minutes. Drain and rinse under cold water to stop the cooking process. Set aside. If using leftover cooked spaghetti, ensure it is untangled and ready to incorporate.

In a large, ovenproof nonstick skillet, heat the olive oil over medium heat. Add the finely chopped onions and sauté for approximately 10 to 12 minutes, stirring occasionally, until they become golden and tender. Transfer the onions to a bowl and allow them to cool slightly. Wipe the skillet clean with a paper towel.

In a large mixing bowl, whisk the eggs and milk until well combined. Stir in the grated Parmesan cheese, chopped parsley, basil, salt, and black pepper. Add the cooled caramelized onions to the mixture. Gently fold in the cooked spaghetti, ensuring the pasta is evenly coated.

Lightly coat the cleaned skillet with nonstick cooking spray and place over medium heat. Pour the egg and spaghetti mixture into the skillet, spreading it into an even layer. Cook undisturbed for 3 to 5 minutes, occasionally rotating the pan to ensure even browning. The base should be golden and mostly set.

Place a large plate over the skillet. Using oven mitts, carefully invert the skillet to transfer the frittata onto the plate. Re-spray the skillet with nonstick spray, then gently slide the frittata back into the skillet, uncooked side down. Continue cooking for an additional 3 to 4 minutes, or until the bottom is golden and the center is fully cooked.

Transfer the frittata to a serving platter. Garnish with diced tomato if desired. Slice into wedges and serve warm, at room temperature, or chilled.