Place olive oil, onion, celery, and a pinch of salt into a large heavy saucepan or Dutch oven over medium-low heat. Cook, stirring occasionally, until onions are very soft, about 15 minutes.

Meanwhile, pour tomatoes with juice into a large bowl and use your hands to crush tomatoes until they look puréed. Set aside.

Mix garlic into vegetable mixture in the saucepan; cook until fragrant, about 1 minute. Stir in sugar, 1 teaspoon salt, anchovy paste, white wine vinegar, Italian herbs, and red pepper flakes. Increase heat to medium; cook and stir just until liquid has evaporated.

Mix in tomato paste until incorporated. Stir in hand-crushed tomatoes and parsley; bring to a boil. Reduce heat to low and bring to a simmer. Cook, stirring occasionally, until sauce thickens and flavors meld, about 1 1/2 hours. Add a little water as sauce cooks down to reach desired consistency.