Heat 3 tablespoons of olive oil in a large Dutch oven over medium-high heat. Season beef with ¾ teaspoon salt; brown in hot oil (about 4 minutes per side).
2 ½ - 3 lb. chuck roast
Remove meat to a platter.
Reduce heat to low; add onions and additional ¾ teaspoon salt. Stir frequently, scraping bits from the bottom of the pan with a wooden spoon as the onions cook and caramelize for 25-30 minutes. NOTE: If you don't have the time or patience to cook the onions for this long, that's fine -- just sauté them for about 7 minutes (until tender). The caramelizing adds extra rich flavor, but it will still be delicious with a shorter time too!
3 Vidalia onions
Add garlic, carrot and celery; cook for 2 more minutes.
3 cloves garlic, 1 stalk celery, 1 carrot
Clear space in the bottom of the pot; add tomato paste, and cook, stirring, for 2 more minutes.
6 oz tomato paste
Add wine and deglaze the pot by scraping up bits from the bottom of the pot with a wooden spoon.
½ cup red wine
Simmer for 3 minutes. Return meat to the pot; add 2 ½ cups of water, Parmesan cheese and crushed tomatoes. Reduce heat to very low; cover halfway (leaving the lid ajar to let the steam escape). Simmer for about 3 hours, or until meat is fall-apart tender.
¼ cup grated Parmesan cheese, 2½ cups water, 28 ounces crushed tomatoes
Discard the garlic cloves. Remove meat to a rimmed baking sheet (or cutting board) and shred with two forks. Return shredded beef to the pot, and stir in remaining 1 ½ teaspoons salt. Serve over pasta.