Fill a large pot with cold water, add a tsp. of salt and bring to boil for the pasta.
In a large, high-sided pan preheated to medium-high, cook the beef with the olive oil for about 2 minutes, until almost cooked through. Add the chopped onion and carrot and let cook about 5 to 7 minutes, or until the onions and carrots start to cook down and soften. Season with lightly with salt and pepper.
Add the wine and cook for 1 minute. Add the crushed tomatoes and garlic, and turn the heat to medium. Partially cover and cook for about 30 minutes; stir periodically.
After 30 minutes, season with salt and pepper and add the peas. Add the pasta to the boiling water. Cook the peas in the sauce for the same amount of time it takes for the pasta to cook.
Once the pasta is cooked al dente, turn the heat off on the sauce. Drain pasta, toss with a little olive oil and serve on plates. Top with sauce, and fresh basil and freshly grated parmiggiano reggiano, if desired.