In a large non-reactive container, lay tomatoes in a single layer. Sprinkle with salt, cover, and let stand 24 hours.
Remove tomatoes from container and drain, squeezing gently. Let rest in a colander for 20 more minutes to remove as much liquid as possible.
Combine tomatoes, chiles, vinegar, and water in a separate non-reactive container. Add additional vinegar and/or water to completely cover tomatoes. Cover and let stand 12 hours.
Drain tomatoes in a colander. Press the tomatoes by placing a plate on top and weights on top of that. Let stand 4 hours.
In a separate bowl, combine the oil, garlic, oregano, and black pepper.
Transfer tomatoes to a jar, packing the remove excess air, and cover with olive oil.
Made with a mixture of San Marzano and chocolate cherry tomatoes (mostly San Marzano). Used rice wine vinegar and two dried, whole chile de arbol.