Cutting boards come in a wide variety of sizes, and you should be able to find one to fit the space; they even make them specifically for this purpose. This frees up counter space, and in a sense extends it, since fitting the board over the sink means the sink can catch anything that falls through while you cut.
Three Kitchen Storage Tricks That Free Up Space

Keeping the kitchen clean and tidy is a job we often avoid, but it pays off in terms of time saved. It's faster and easier to prepare meals, and you can spend more time relaxing and savoring the results. Try these kitchen storage and organizing tips to make life easier.
A Cutting Board That Fits Over the Sink
Make Use of Your Ceiling
Overhead racks are popular with people who live in small spaces like RVs. You can use these same types of racks in any kitchen. It's a wonderful way to get your pots and pans out of the way, but still keep them well within reach.
Use Tension Rods in Cabinets and Cupboards
Place them horizontally and use them to hang cleaning products and other items that can hook around them. Or place them vertically to support pans, plates, and other dishware. It's an easy way to add functionality to any cabinet space.
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