In a large rectangular container, mix together the oil, vinegar, oregano, and salt. Place the tomato slices and onion in the marinade. Cover and shake it around a bit to coat. Let marinate overnight or for at least 2 hours. Let the tomatoes sit out to come closer to room temperature before you use them (this helps improve the flavor and melt the olive oil if it has hardened).
In a medium bowl, mash up the white beans into a paste. Stir in the vinegar, oregano, garlic, and salt until combined.
Spread the bean mash on one piece of toast and mash avocado onto the other. Top one slice with lettuce and/or sprouts, marinated tomato slices, and onion. Place basil on top of the other slice, if using. Form the sandwich, press down to compact it, and cut in half.
I like to dip the sandwich into that marinade as I get towards the end. You can also use that marinade for a simple salad or for dunking bread.