Bring a large pot of water to a boil.
As soon as you put the pot over the heat, start cooking the sauce. In a large skillet or saucepan, heat the olive oil over medium heat. Add the garlic and onion and sauté until the onion turns translucent, 2 to 3 minutes.
Add the beef and shiitake mushrooms, raise the heat slightly, and sauté, stirring constantly and breaking up the meat into fine particles with a wooden spoon, until the beef has uniformly lost its pink color, 5 to 7 minutes. Carefully pour off any fat.
Return the skillet or pan to the heat. Add the tomatoes, tomato paste, oregano, basil, sugar, and bay leaves and stir well. Bring to a boil, reduce the heat to maintain a brisk simmer, and cook until the sauce is thick, 15 to 20 minutes.
About halfway through the sauce's simmering, add the pasta to the boiling water and cook until al dente, following the manufacturer's suggested cooking time.
Before the pasta is done, taste the sauce and season with salt and pepper to taste; remove the bay leaves. As soon as the pasta is done, drain it and toss with the sauce. Serve immediately.