Heat the olive oil in a large cast-iron pan or heavy saucepan over medium-high heat. Add the beef in batches if needed, then press it flat and let it brown well underneath. After that, turn it, break it up into small pieces, and transfer it to a bowl with a slotted spoon.

Finely chop the carrot, celery, onion, and garlic in a food processor until they are almost minced.

Lower the heat to medium. Add the butter and a little more oil if needed, then cook the vegetables with about 1 teaspoon sea salt for about 10 minutes until they are soft and fragrant.

Stir in the tomato paste and cook for a few minutes until it darkens slightly.

Add the diced tomatoes, whole herb sprigs, bay leaves, and sugar. Return the beef to the pan, mix well, and season with salt and pepper.

Cover the pan and cook on very low heat for about 1 1/2 hours, stirring occasionally.

Uncover the pan and cook over medium heat for about 30 minutes or until the sauce is thick. Taste and adjust seasoning if needed.

Bring a large pot of water to a boil and add 1 teaspoon fine salt. Cook the spaghetti 2 minutes less than the package says.

Warm the sauce and add the spaghetti straight to the sauce, tossing until well coated. If the sauce seems too thick, loosen it with a little pasta water.

Serve topped with parsley, extra herbs, and Parmesan.

Keep leftovers in an airtight container in the refrigerator for up to 4 days.

Freeze portions for 3 to 6 months. Let it cool first, then pack it into freezer-safe containers.

Reheat on the stovetop over low heat, adding a splash of water if needed, or in the microwave in short bursts.