Start by cutting your beef chuck into 1-inch cubes. Chop the onion, dice the carrot and celery, and mince the garlic.
Heat 2 tablespoons of olive oil in your heavy-bottomed pot over medium-high heat. Add the beef cubes in batches to avoid overcrowding and brown them on all sides. Once browned, transfer the beef to a plate and set aside.
In the same pot, add the chopped onion, carrot, and celery. Sauté until softened and fragrant, about 5-7 minutes. Add the minced garlic and cook for another 1-2 minutes, stirring frequently to prevent burning.
Return the browned beef to the pot. Pour in the crushed tomatoes along with 1 teaspoon each of dried oregano and basil. Stir to combine and season with salt and pepper. Bring the mixture to a gentle simmer.
Reduce the heat to low, cover the pot partially, and let the ragu simmer for at least 1.5 to 2 hours. Stir occasionally and add a splash of water if the sauce becomes too thick.
About 15 minutes before the ragu is done, bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente. Drain and set aside.
Taste the ragu and adjust seasoning as needed. Toss the cooked penne pasta into the sauce, coating each piece generously. Let it sit for a minute on low heat to marry the flavors.
Serve the Italian Beef Ragu with Penne in bowls, topped with freshly grated Parmesan cheese and a few fresh basil leaves. Enjoy immediately!