In a large pot of salted boiling water, cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the sliced onions and 1/2 teaspoon of salt. Cook, stirring occasionally, for about 15-20 minutes until the onions are golden brown and caramelized.

Sprinkle the sugar over the onions and continue to cook for another 5 minutes, stirring frequently. This will enhance the sweetness of the onions.

Add the minced garlic and red pepper flakes to the skillet, cooking for an additional 1-2 minutes until fragrant.

Add the cooked pasta to the skillet along with the reserved pasta water and the remaining tablespoon of olive oil. Toss everything together until well combined. Adjust seasoning with salt if needed.

Serve the pasta hot, topped with grated Parmesan cheese and fresh parsley for garnish.