A secret ingredient makes this meaty sauce SUPER meaty tasting: mushrooms!
In medium bowl, combine beef, water, 1 teaspoon salt, and baking soda. Use rubber spatula to mix until well combined. Set aside.
Use chef’s knife to trim off ends of mushroom stems and discard. Cut mushrooms in half if small or into quarters if large.
Add mushrooms and onion to food processor. Lock lid into place. Hold down pulse button for 1 second, then release. Repeat until vegetables are chopped fine, about eight 1-second pulses. Remove lid and carefully remove processor blade (ask an adult for help).
In large pot, heat oil over medium heat for 1 minute (oil should be hot but not smoking). Use wooden spoon to scrape mushroom mixture into pot. Cook, stirring occasionally, until vegetables are softened and well browned, 8 to 10 minutes.
Stir in garlic, tomato paste, and oregano and cook for 1 minute.
Carefully stir in tomato puree, diced tomatoes and their liquid, and ½ teaspoon salt. Use wooden spoon to scrape up browned bits on bottom of pot. Bring to simmer (small bubbles should break often across surface of mixture).
Reduce heat to low. Cook, stirring occasionally, until sauce thickens, about 30 minutes. Turn off heat.
Meanwhile, set colander in sink. Add 4 quarts water to second large pot. Bring to boil over high heat. Carefully add pasta and 1 tablespoon salt to pot. Cook, stirring often with wooden spoon, until pasta is al dente (tender but still a bit chewy), 10 to 12 minutes. Turn off heat.
Use ladle to carefully transfer ½ cup cooking water to liquid measuring cup. Ask an adult to drain pasta in colander. Return drained pasta to now-empty pot.
Stir Parmesan cheese into sauce. Add sauce and ¼ cup reserved pasta cooking water to drained pasta (ask an adult for help). Use tongs to toss until pasta is well coated with sauce. If needed, add remaining ¼ cup pasta cooking water, a little bit at a time, until sauce is loosened slightly and coats pasta well. Serve with extra Parmesan cheese.