Overripe tomatoes may be a little too soft for a sandwich, but according to the good folks at Bon Appetit, there's no reason to chuck 'em. You'll want to rinse or cut off the mould, of course, but once that's taken care of you're just hours away from delicious tomato water, a light but umami-packed liquid perfect for sauces.
You should check out the link below for details and fancy variations, but the method is pretty simple. First, you're going to wash or scrape off any mouldy bits. Then simply chop them up, salt to help draw out the juices, blend it all together and let it strain overnight.
You can spoon tomato water over light pastas, toss it into tuna salads, or (my favourite tip) sub it for olive brine in a dirty martini for a fresh cocktail that tastes straight from the garden.
When Life Hands You Overripe Tomatoes, Make Tomato Water [Bon Appetit]