Heat the olive oil in a large pot over medium heat. Add the finely chopped onions and cook them slowly, stirring occasionally, until they are soft and translucent (about 15-20 minutes).
Add the minced garlic and beef cubes to the pot. Stir well to combine, ensuring the beef is coated with the onion mixture.
Season with salt, pepper, and thyme. Continue to cook, stirring occasionally, until the beef is browned on all sides (about 10 minutes).
Pour in the white wine, scraping up any browned bits from the bottom of the pot. Allow it to simmer for about 5 minutes, letting the alcohol evaporate.
Reduce the heat to low and cover the pot. Let it simmer gently for around 1.5 hours, stirring occasionally. Add a splash of water if it becomes too thick.
While the sauce is simmering, cook the pasta according to the package instructions in salted boiling water until al dente. Drain and reserve a cup of the pasta cooking water.
Once the Genovese sauce is ready, combine the drained pasta with the sauce in the pot. If the sauce is too thick, add a little reserved pasta cooking water to reach the desired consistency.
Mix well to ensure that the pasta is evenly coated with the sauce. Serve hot, with grated Parmesan cheese on top if desired.