In a blender or food processor, roughly puree the tomatoes with their juices. (If the tomatoes are packed in puree rather than juice, you might need to add a little water to the sauce to thin it out a bit.) Put them in a 6- to 7-quart slow cooker.

In a sauté pan over medium-high heat, heat the oil, then add the onion and garlic and season lightly with salt. Cook, stirring frequently, until the onion starts to become translucent, about 4 minutes. Scrape the mixture into the cooker.

Add the basil sprigs, oregano, 1 teaspoon salt, and ½ teaspoon pepper.

Cook, covered, on the low setting for 6 to 8 hours. If the sauce is too thin after 6 hours, cook on the high setting with the lid on sideways for 1 hour, or until thickened to your liking. Remove and discard the cooked basil.

Stir in the chopped basil, season again with salt and pepper, and add a bit of sugar or the baking soda if the sauce is too acidic.

Serve immediately, or can the sauce for future use, or freeze it in small containers for up to several months.