Heat olive oil in a large skillet over medium heat along with tomatoes and broccoli until 3 minutes. Remove the pan from the heat after making sure the mixture is well cooked.
Fill a large pot with water and boil it. Add spaghetti and one tablespoon of salt in it. Cook the spaghetti and rinse in a colander with water at room temperature. Next, prepare the ingredients: Cut the bacon into thin slices. Simmer until it is almost cooked (cooking time indicated in the intro paragraph).
Prepare carbonara sauce. Fold the pasta in a colander and add vegetables to the pan. Place the pan over low heat and add beaten eggs, cheese, cream and a tablespoon of salt. Toss the spaghetti in the pan, until the pasta has absorbed the sauce (about 1 minute). To do this, carefully whisk the eggs and add salt. Add the cream and eggs exactly half the grated cheese. If the bacon has cooled down, heat it in the microwave and mix it with the sauce. Add the sauce to the pasta and bacon.
Serve immediately, sprinkled with freshly ground pepper. Put the finished pasta on a plate.