In a saucepan, heat the olive oil over medium heat. Add the onion and garlic, and cook until soft and light golden brown about 8 to 10 minutes. Add the oregano and carrot, and cook 5 minutes more, until the carrot is soft. Add the tomatoes and juice and bring to a boil, stirring often.
Lower the heat and simmer for 30 minutes.
Pour in the cream and season with salt.
Cook your pasta while your sauce is finishing cooking. Strain pasta when it is done cooking.
Top the pasta with the sauce and garnish with the basil leaves and cheese.