Also known as Möbius strip bagel. More room for cream cheese!
The real question is: is it worth it? How much more spreading room do you actually get? Mathematician Antonio R. Vargas has done the calculations, and they get quite complex, veering into calculus. On a webpage hosted by Dalhousie University, Vargas concludes that “the ratio of the surface area exposed by cutting along the two-twist Möbius strip to the area exposed by cutting the bagel straight in half is approximately: 1 + 1/6 (heights/width-height)2.”
To make a long story short, the amount of spreading surface you get depends on the size of your bagel, but it will always be more than if you had cut it in half.