As you know, we live for months each year in Airbnbs around the world. Most Airbnbs come with a fully-equipped kitchen with pots, pans and dishes.
However: I hate using other people's cutting boards. And Airbnbs rarely have sharp knives, or any tool for sharpening knives. Life is too short for dull knives.
That's why I recommend to all gastronomads to carry your own cutting board and knives.
One great option is the Gerber Freescape Camp Kitchen Kit.
It's basically a briefcase with a handle, where the top is a cutting board. Inside are two good knives in a locking drawer and integrated ceramic knife sharpener.
I also recommend that everybody carry eating utensils.
One way to minimize what you carry is an integrated spoon and fork — a spork.
The Sparkfun S.H.O.V.E.L. (for "Semi-Horned Oblong Versatile Eating Ladle") is a titanium spork with a serrated knife, a bottle cap opener, and six feet of red paracord!
Here's all the gear I use and recommend.