Simple Italian-Style Meat Sauce

Process mushrooms in food processor until finely chopped, about 8 pulses, scraping down sides of bowl as needed; transfer to bowl. Add bread, milk, 1/2 teaspoon salt, and 1/2 teaspoon pepper to now-empty processor and process until paste forms, about 8 pulses. Add beef and pulse until mixture is well combined, about 6 pulses.

Heat oil in large saucepan over medium-high heat until just smoking. Add onion and mushrooms and cook, stirring frequently, until vegetables are browned and dark bits form on pan bottom, 6 to 12 minutes. Stir in garlic, tomato paste, and pepper flakes; cook until fragrant and tomato paste starts to brown, about 1 minute. Add reserved tomato juice and 2 teaspoons oregano (if using dried, add full amount), scraping up any browned bits. Add meat mixture and cook, breaking meat into small pieces with spoon, until beef loses its raw color, 2 to 4 minutes, making sure that meat does not brown.

Stir in crushed tomatoes and diced tomatoes and bring to simmer. Reduce heat to low and gently simmer until sauce has thickened and flavors have blended, about 30 minutes. Stir in Parmesan and remaining 1 teaspoon oregano; season with salt and pepper to taste.