In a medium skillet, heat the olive oil over medium heat. Add the onion and carrot and cook for 5-7 minutes. Add garlic, red pepper flakes, and salt. Cook for 1 minute longer.
Add the tomatoes (with juices) and sugar. Use a wooden spoon to break up the tomatoes. If you want a smooth sauce, blend sauce in a blender. Cook for 8 - 10 minutes. Add 1 cup of water. Continue to cook for another 10 minutes, until sauce begins to thicken.
Season to taste and add fresh basil.
Meanwhile, in a large pot, bring water to boil over high heat. Generously add salt to the water. Once the water is boiling, add the pasta and stir. Cook the pasta until al dente, according to package instructions. Drain.
In a large bowl, toss the pasta with 3/4 cup of Parmigiano-Reggiano Cheese. Pour the sauce over the pasta. Sprinkle remaining cheese on top of sauce and serve.