Make a cut through it shaped like a mobius strip - that is, a single 180 degree rotation instead of going the whole 360 degrees shown here.
To think about it another way, imagine if you took a mobius strip and constructed a semicircular lump of bread on the surface, extending it around until it connects back to itself. You've made a bagel!
Now take the mobius strip out of the middle, and the gap it leaves is the cut you're asking to make.
Potentially interesting to anyone with an oven, if you can capture 1% of that market you'll be rich!
I'd suggest raising a few million in seed funding and renting an office in downtown SF. If it doesn't pan out you can pivot into math-related silicone ice cube trays.
To think about it another way, imagine if you took a mobius strip and constructed a semicircular lump of bread on the surface, extending it around until it connects back to itself. You've made a bagel!
Now take the mobius strip out of the middle, and the gap it leaves is the cut you're asking to make.